For myself...
I am on record saying that the Reynolds film's biggest sin isn't that it's some horrible abomination. It's just thoroughly forgettable because it's so bland. It's the NOW THAT'S WHAT I CALL MUSIC compilation of super hero films. Paint by numbers all around, which is saying something cuz when it comes to super heroes in general there's a lot of tropes/cliches already.
I don't know if we'll get Hal, I don't know if it'll be John, or a combo. In either case what should be important when it comes to a film featuring them as main protagonists is this: What does it mean to be a Green Lantern, and how does that play into the characterization that we see?
Delve into that and you are ahead of the game. We all know the lore. A GL is chosen via a technology billions of years in advance of our own, tapping into the very will to live of all sentient beings in the universe. To be chosen means that the candidate must have great will power, be honest and have great control over their fear, i.e. be "fearless".
Well what does that mean for a character? How is that expressed to the audience? Surprisingly I think naturally this could make a person like Hal Jordan or John Stewart unlikable from time to time. A person that is fearless and honest all the time might get on your nerves or at least be hard to be around sometimes. When your lady friend asks you if the clothes she's got on makes her look fat, if you want her to remain your lady friend a lot of us are all, "No... NO. You look great in that." Hal Jordan? Well, he's gonna tell you the truth and he's fearless in facing the consequences. These are defining aspects of such a character and you have to find some way to make those aspects come through in a three dimensional way in live action film. One thing really bungled in the 2011 film was that. I mean, we actually had a GL film where Hal Jordan does the "I don't know if I can do this" BS of so many other super hero films. The last character who in his first film that should have pre-game jitters is HAL JORDAN.
I think that if we get a new Sinestro (and explore the additions Johns made to the mythos) then this becomes even more incumbent on the story, to explore what it means to be a GL. Remember, it's the morality of Sinestro that separates him from Hal/John/Kyle/Guy. Being honest, fearless with great will has less to do with ethics than we would like to believe. Characters that are the antagonists/villains are no less steadfast in their beliefs or incapable of great acts of will or courage than the heroes. Sinsestro honestly believes himself in the right. Show that. Show that the villain is capable and as driven as the hero.
So that's one thing. While I can agree that a good way to go is indeed the "en media res" route, with the Earth GL chosen and active and already trained showing the newly minted human GL the Ropes. That said, I can also see a bit of a rehash of the origin so that we could get something the Reynolds film failed to do: Give us a good training sequence that helps to further define the hero's powers and personality. One of my fave additions to the mythos is Johns saying "Yeah, nobody can just pick up the ring an go toe to toe with a Manhunter army. Being a GL is being a badass that uses a weapon that literally takes your all to control and master." Maybe we need a good chunk of the film to be about his training, just to help the audience grasp that as well as further delineate the character(s). If we treat the GLC as a military service then look no further than films about any nation's armed forces to see the beats such a film might ape. You have induction, training, and then at some point you send the characters off to some conflict where seeds laid in the first two thirds often pay off. I also think that maybe something showing the day to day grind of being a GL would help. That sort of HILL STREET BLUES vibe only with "space cops". The Guardians view things with the eyes of immortal beings that are only slightly younger than the universe itself, but the rank and file GL's are creatures just doing a job. Plus with that sort of feel you can have some fun as well as give the audience something they can easily wrap their heads around. For all it's mysterious alien nature, Oa is essentially the main precinct for a pan-universal police force. Show it like that.
I think it goes without saying that most fans would like to see a GLC film that focuses on events in space rather than Earth. So I will just add my voice to that chorus.
Another thing that needed more definition (and thus perhaps some exposition or a montage giving us an idea of their past) is The Guardians themselves. They were far too mysterious and voiceless in the Reynolds movie. I don't know if you go with a Ganthet as a more approachable Guardian or what, but they have to be and do more in the film's story than sit in some comically high chairs.
Now as for the powers of the ring itself? Yeah, they need to REALLY NEED to put GL into that Superman bad ass level of power as we saw in MAN OF STEEL. Show that it's not just making cute green objects. Show that it truly lives up to the title "Most Powerful Weapon In The Universe"... And don't shirk on that in subsequent films, which is to say, no BS Batman defeats GL in a yellow suit or palms the ring off him.

Batman is an extraordinary individual but Goddamnit, so is GL. Don't job out the character in any way just to make an already popular character look good.
Those are just my baseline thoughts having pondered the GL film from 2011 for so long.