First up, I would place them into the MCU, no doubt but I honestly think the MCU connection is the least important aspect. The franchise could work as either a film or a streaming series though reasonably speaking a show would require an incredibly high budget. Let's start off with tone.
Tone:
I see the tone as being a mix of the nonchalance cool of OCEAN'S 11 mixed with the high tech tales of exploration one had on Star Trek: The Next Generation. The characters are all witty banter and creative solutions that take on situations one would expect from a group tackling all sorts of scientific mysteries and attempting to expand the horizon of knowledge.
I would go for background music that alternates between a big brassy swing sound like Sinatra in the early 60's and a more subdued techno inspired one. Think half the time it's Henry Mancini or Lalo Schifrin and the other half it's Daft Punk. Above all the connection between the main characters needs to be front and center. This is a "family". There is a deep connection between all of them. Now, that doesn't somehow preclude conflict, drama and personality clashes. If anything it guarantees it! That said that element cannot come off as forced or unearned. Ben's resentments and depression, Reed's guilt, Johnny's impulsive flippancy and Sue caught in the middle of it all could be done in a way that is feels very manufactured. This is something even the comics often stumble with. I would show that each character has a bond with the other three in ways that are unique and understandable despite the out there circumstances they always find themselves in.
Basic Set-Up:
I think I would start en media res with the team having the origin told in flash backs, whether film or TV series. If a film, those flash backs would be to simply fill in plot and background info. On a TV show I think I would take the LOST approach and have pivotal information revealed during said flashbacks. The flashbacks would be about both the lead up to them gaining their powers and the aftermath but also character history from long before the group got together, ranging from childhood to college age. Based out of Manhattan the team's headquarters of the Baxter building is more than just a place to hang their hats. It is the central hub for cutting edge theoretical research, which cover particle physics, nano tech, artificial intelligence, genetics, and astrophysics, except that it's not all just theoretical. At any time of the average work week great minds of science, politics and celebrity can be found coming and going from the ground level entrances. Of course that's when the FF want people to know they have guests. And guests aplenty would be an element I would have. Real life celebs, politicians and scientists along with the FF's fictional alums like Hank Pym and Tony Stark would always be around conferring with Reed and the team. I think the team needs to be seen as "cool" and celebrity pop ins would add to that. People come and go to get the team's help or assist them with something but Reed is also smart enough to harness another form of power the team possesses to do good. The power of celebrity and wealth. To that end the Fantastic Four Futures Foundation is the name under which the team operates it's charitable and philanthropic enterprises. If a TV show the FFFF would be a very prominent aspect. On a show you can have the FFFF lead to all kinds of stories. If a film it would be a bit more of a background element. Action would be of the four quadrant manner, not too gory or over the line but it has to be thrilling. The story has to be about sci fi wonder and the dangers that can come with it.
The Team:
1. Johnny Storm/The Human Torch- Okay I'm gonna get a huge pet peeve off my chest about the usual depiction of Johnny... HE SHOULD NOT BE A ****ING IDIOT. Look I know it's can seem to a film maker that with one of the FF being the literal smartest man in the world that it's natural to have some other member be thick as a brick. I get it but it irks me no end in toon and movie versions where Johnny is just a fool that's there to bring laughs.
Johnny of course can be used for comic relief, and of course he's not at Reed's level intellectually but why does that then also mean he's a dope with no common sense who comes off as if he has no real respect for any of the others so often in adaptations? Well I ain't having none of that. Johnny would be called on for lighter material and to bring humor but it shouldn't really ever be at the expense of being a real character, or undermining his or other character's inherent dignity. In my conception of a live action FF, whether TV/Streaming or Film I see Johnny as an honest to goodness teenager. Not an astronaut, not a pilot, not a peer in any way close to the others in age. He's a kid. Full stop. Now Johnny acting flip, making huge mistakes or acting out fits and I think the audience would find it more acceptable. He's well under 21 years old. As such, his emotional tool box isn't fully loaded yet. He doesn't have the natural stockpile of experiences to draw from that the other members do. This makes him rash, but not acting just to do dumb stuff. He's literally ignorant, but not thick headed stupid. As a kid he's likely to overcompensate in all manner of things both to positive and negative effect. He loves his sister deeply as he was convinced for so long that they would only have each other in this world. Now there's a man in Sue's life. How does Johnny handle that? I actually think that instead of headless rebellion that Johnny welcomes Reed, even idolizes him, though he's got to keep a "too cool for school" attitude as a front. Remember, he's a teen overcompensating. But he embraces Reed. Sue is more than just Johnny's older sister. She's been his defacto mother as well and he wants her to be happy. In Johnny's eyes he wants that family unit to be complete and Reed isn't just his brother in law, he's a father figure. One that he butts heads with but that is what happens between father's and sons all the time. Johnny also LOVES having super powers and the celebrity that comes with it. To that end instead of being indifferent to Reed's technobabble, at least when it comes to his powers Johnny soaks up Reed's observations like a sponge. He's fascinated by what he can do and listens to Reed so that he can learn to do even more. Johnny is also a gear head and I would make this a point of commonality between he and Ben. Johnny is never going to get the concepts of sub atomic particles but he understands the engineering of modern cars and is even picking up some aeronautics form Ben. Johnny knows Ben misses his life as a pilot and so he always asks him about stories from that time in Ben's life as they go about working on the classic cars that are Johnny's hobby. Johnny has reservoirs of compassion but again his youth trips him up. He really feels for Ben but in trying to get him out of the funks that sometime overcome him he ends up appearing to just be a snot nosed punk to those on the outside looking in. He's just trying to do something in a situation he feels powerless in where someone he respects and loves is being tortured by their circumstances. Johnny might tease Ben to take his mind off of his situation, but if someone else does it even half hearted he will blow his top at them. I don't have any particular actor in mind for Johnny or any of the other members but if I had to put down the type I guess I would go for someone like a light haired Justin Long meets Sean William Scott type from the early part of their careers. Somebody that can get the youthful aspects of the character across well, both the genuine and the flippant and can handle both the dramatic and light shades.
2. Ben Grimm/The Thing- The character that always evokes the most pathos, but also the most fun and relatable character. Ben is the guy that is the natural protector type since he was young. He was the type that for sure bought into all sorts of common held stereotypes about being a man and he did his damndest to live up to them to the max, but not in a way that's all about aggrandizing himself at the expense of others. For Aunt Petunia's favorite nephew all that male energy is about being strong enough and stoic enough to handle what ever life throws your way so you can be there for your family but also so that you are tough enough to protect those less fortunate or weaker than yourself. Ben is about commitment, and about taking the slings and arrows of life as they come because that's what a man does.
This is a bit old fashioned in it's outlook but with Ben it works. That's not to say he doesn't have the signature Marvel Comics angst. No, it's there in spades. He's just really good at covering his disgust and depression at what has happened to him for the outside world. So he throws himself whole hog into the world of super heroics a celebrity and attempts to live his life as though nothing has changed all that much for him despite the reminder he gets whenever he looks in a mirror. Ben is the most New Yawk of the four.
He is an embraced and beloved figure of everyday folks in NYC. He's on a first name basis with every food vendor and hot dog cart owner in a ten block radius of the Baxter Building. TMZ and other tabloid media stake out the building's entrance to get video of the affable "freak" who tries to live life as though he's not a giant super strong orange rock colored being. He goes about his life trying to live it the way he did before the accident. This leads to inadvertent humor as Ben clothes himself in comically over sized NYC sports Jerseys or everyday clothing. Ben loves kids, again that natural protector part of him, so he often spends his off time donating himself to the FFFF charities that deal with handicapped and disfigured children. Ben also feels that he'll never have children of his own now. As such he attempts to pass on knowledge and wisdom of the hard earned kind to Johnny as much as he can. Ben has resentments against Reed. Who deep down would not? But he's also aware that his friend is beating himself up inside everyday that he cannot find a cure. Ben knows that while Reed is a man of total rationality somewhere in his psyche Reed thinks that Ben's condition and the inability of him to find a cure despite all his brilliance is a punishment the universe has doled out for Reed's arrogance about his towering intellect. As such, while Ben feels bad about being transformed, he actually feels worse for Reed and keeps a stiff upper lip to not hurt his feelings. This mix of inner turmoil and the way that Ben's personality was even before the exposure to cosmic rays means that of them all Ben is always ready to leap head first into some adventure. If he's doing something, if his big rocky hide can be useful then that's less time he has to contemplate how his deformity has affected his life. I think they hit the nail on the head with Michael Chiklis in the Story films casting wise but he was not well served by those scripts. So I would keep the casting in that wheelhouse.
A big bear that can be both menacing and lovable in equal measure.
3.Susan Storm-Richards/The Invisible Woman- Sue is the member of the team that is dealing with it all. And I do mean everything. She is not a scientist as in the Story or Trank films. But what she does have is a natural skill at organization and delegating responsibility. The team but also the Baxter Building and the FFFF could not work without her constant efforts to keep every plate spinning. Sue has a natural gift for PR, and spin, but not in the negative way we think of in say politics. No, she's great at making her case for something and being able to negotiate among people to get it done. It could be an outgrowth of navigating the personalities of the FF or it could be an inborn talent. In any case she is through either nature or circumstance an outgoing extrovert. In NYC she's a sought after celebrity that can bring focus and action to what ever cause the FFFF has in it's cross hairs. She's in a way the team's therapist too. Everyone, even Reed goes to Sue to cry on her shoulder or to complain about the others. This can be overwhelming but Sue keeps her frustrations well hidden under a facade of being a modern woman that's got it all together. She's the one member that thinks it's all on her to make it work when they are not out on an adventure. The adventuring super hero thing is Reed's department. Her domain is everything else that makes the adventures possible. Her marriage, raising her brother, looking out for Ben, running the charities, administering the board for the research the Baxter Building does. She does it all because she has to, which is what many women that balance career and home will tell you. Her codename is a two edged sword. She does so much and does it flawlessly she sometimes feels she is invisible. It's like as though the others often don't get that the team operates as it does due to her herculean efforts. The other side of that sword is that there are days she wishes she could just disappear and let all of this weight be on someone else's shoulders. Sue is not a scientist but she is fascinated by Reed and how he views the world, existence in total. Reed is devoted to truth above all, and in searching for those truths he reveals new wonders to the world. She may get frustrated with the man but he's someone she has complete and total faith in. Sue's ability to improvise also serves her well in the use of her powers. Perhaps more so than even Reed she is the one member of the team that can use her powers in the most versatile way and she is the most inherently dangerous member of the team, something to often overlooked by the FF's adversaries, even Doom. I guess in casting you need a mixture of the gravitas that a Charlize Theron has (and had even when she was quite young) and the everyday womanly smarts and comic timing of a Sarah Chalke type.
4. Reed Richards/Mr. Fantastic- Oh boy... Where to start? Okay first off Reed has got to come off a lot less like an egghead and a lot more cool.
Perhaps to the point of arrogance even. If you look at recent adaptations getting across how amazing Reed is because of his intellect more than his power set is seemingly difficult. Making smart cool and interesting is a balancing act, with it's own pitfalls writers fall into regularly. Again, I think the key though is to make Reed and his intelligence cool. The difficulty is not doing it in the way that's currently en vogue. More often than not these days you find fictional geniuses as being depicted as either snobby, arrogant asshats that are separate and cut off from society or others in some way usually emotionally or they are geniuses but lack some aspect of common sense. In any case there is this very ham fisted rule in a lot of stories where there is some heavy personality price to be paid for being so much smarter than everybody else and while it can work to make Cumberbatch's Holmes cool, or Dr. House ect. it also tends to make them off putting in some way.
The other type is the usual socially awkward nerd trope. None of that should apply to Reed. No, for Reed I think the template is another BBC regular...
Doctor Who, or more specifically the affable and endearing take of the Matt Smith/David Tenant years of the Timelord. Here was a super genius that was a little off, sure, and still a science genius but never an ass to those whom it was unwarranted to be so. Funny, always thinking, always observing always game to find out something new. That's Reed to T if I were in charge of the character. I would leaven that with a pinch of social awkwardness but maybe not even that. I would say that Reed is eternally "un-hip" but he's always "cool". Reed isn't keeping up with popular culture because he's unconnected to the wider world and culture. He's more than aware. He just realizes it doesn't really matter. But he is grounded into what does, and that goes beyond his research. He calculates it all into his actions. He isn't blind to politics, nor human emotions and interactions. That sort of analysis on the fly is what gives him such an edge in his adventures and endeavors, both before he gained his powers and after. That's why again, flashbacks are really important. Establish that Reed was a genius that thrilled to adventure as much as to research. Make it that he sees no appreciable difference maybe?
All knowledge is self knowledge could be part of his personal credo. He's not a cold man. His emotions are as keyed into things as anything else. He is fulfilled by finding out new things and going new places and he wants others to be just as excited as he is. He's a rational man but he sees a "spiritual" value in scientific quests, and a beauty in the truth science uncovers about the universe and sentient existence in it. This also makes him the type that takes a lot of effort to surprise on his enemies part. Reed even without his power could walk in and out of CIA headquarters and liberate whatever information he wanted to an no one would ever know he was there. Again, like the Doctor... He's just that cool. No, I would have this version of Reed not be simply a forgetful professor type that shuts himself off from his friends and family all the time. If anything this version of Reed is in fact using his brain all the time to try and serve them in some fashion. Cutting them off knowingly or inadvertently would actually be the signs of someone a lot less bright than Reed is supposed to be. No this is a Reed that has a balance between his emotions and his rationale sides. What makes him a genius is that he can actually navigate those two areas equally. Now that brings up some interesting story points once you establish that because now when he gets to a situation where he must choose between the two, where he can't find the way to solve the problem all around you get to see what his choices will be and it's more likely for the drama to work. If we all assume Reed has a huge emotional blind spot and is an absent minded professor type then when he does just that... Who is gonna be surprised? If you establish that he has got his **** together then it becomes a bigger deal when even he can't square a circle so to speak. Above all the actor needed to play Reed cannot just be a nerdy milquetoast. He has to have a charm, even a magnetism, must be good at playing the collected type but also show the commitment to science because he finds it all so wondrous. I honestly don't even know where to start
with the casting. I will say the story films and the show on CN and the Trank films all missed the mark to varying degrees to my eyes.