First of all, I think that the next one should be a reboot, with a new origin, but with a different take on the formula: the origin is shown near the end of the film. 
How? Well, I was thinking of a villain that would be interesting to see Superman fight, and I thought of Eradicator. Here's how I basically see it going: 
At the beginning of the film, Superman is already established in Metropolis, but he's only recently established. He knows he's not from Earth, but he really doesn't know much of anything about Krypton, or where he's from at this point. The romance with Lois is not developed yet either, not on Clark's side, nor Superman's. 
Now, here's the part of my idea you guys may not like: he still lives with his parents. Now I know what you're thinking, "Wtf?" but just let me explain. He stays with them mostly to help his father take care of his mother, whose health is declining a lot. Now, during the course of the film, he does get an apartment, as he's invited Lois to dinner, which she accepts to humor him. 
Anyway, Knowing she won't be around much longer, Martha has Jonathan take Clark outside into the field, and tells him that buried there in the field is the "basket" they found him in. He digs it up (which doesn't take too long for him) and finds the rocket that took him to Earth as a baby. However, he accidentally activates something deep inside it. 
As he lays in bed asleep, he has brief visions in his dreams of a dying planet, and blurry figures he can't make out. He wakes up in a cold sweat just as the rocket takes off on his own. He follows it all the way to the Arctic, and it lands in the distance. Slowly, the environment around it takes on bizarre shapes and forms, and strange structures seem to build themselves. When the Fortress of Solitude is complete, Clark goes inside and finds the rocket transformed into a bizarre iron maiden-like device. 
He then hurries away in time to stop a disaster of some sort, and this is when the relationship with Clark and Lois builds some more, along with his relationship with the Daily Planet. Later in the day, when all seems well and calm (except for Superman/Clark), he goes back to the fortress to find that the great glowing cocoon is shifting. 
The strange, glowing sarcophagus opens, and the Eradicator steps out, a highly advanced android with an A.I. system that creates an almost human personality. It explains to him that he is of a vast alien race from a planet called Krypton, and that he was designed and programmed to nurture him and teach him of his heritage, but that when he entered Earth's atmosphere, his system malfunctioned, and he had to shut down until he could be reactivated. At first, Clark is glad that he has the company, as Eradicator displays a lot of powers not unlike his own. 
The day goes by as usual, with Clark turning into Superman to save a burning school, or something like that, and as usual, he denies Lois the interview she's been wanting. However, he has a harsh episode when the visions return again, and he nearly fails to save Lois from some sort of peril. 
When Clark goes to sleep the next night, the dreams come again, but more fierce and emotional. He confronts the Eradicator about it, and the Eradicator tells him that he's been probing his mind, and feeding this knowledge directly into his memory. He tells the Eradicator that he doesn't want this knowledge, that it's taking a toll on him mentally and emotionally. Eradicator decides that he's not an ally, but an obstacle. Confused by Eradicators behavior, he asks just what it is that he was really sent to do. 
Eradicator reveals his plan: to turn Earth into a new Krypton by terraforming the entire planet in a process that would eradicate all life on Earth, but Superman. A fight scene ensues, but Eradicator manages to overpower him with not only his vast physical powers, but his mental powers as well. Superman has no choice but to flee and recover. 
Eradicator sets his plan into motion, as he begins to grow another Fortress in the South Pole, directly aligned with the Fortress in the North. However, the Fortress destroys a LexCorp research facility, and the public is overwhelmed with fear as the Eradicator tells humanity that all Earth life is to be destroyed. He begins the process, and a strange biological agent is released from both fortresses, and strange bio-engineered, almost mechanical plant-life begins to grow at an incredibly rapid pace. 
Superman, however, after a climactic battle against the strange carnivorous plants, manages to destroy the Southern Fortress. While the world waits in fear of it's doom, Superman knows that the only way to truly destroy the creatures and save the world is to go directly to the source: The Eradicator. Fully charged and ready for battle, Superman flies to the Northern Fortress. He confronts him, saying that he's failed, but the Eradicator has an ace in the hole: he can still turn Earth into a New Krypton by flying into our sun and turning it into a red dwarf star. 
This is when the big showdown in the sky takes place. After the huge fight, the Eradicator knowing that he is about to be defeated, tells Superman something like the following: "I may fail this mission, but for the rest of your life, you're going to wish I hadn't...Kal-El." 
It is here that was see the origin: The Eradicator fills Superman's head with knowledge all at once, beginning with his father. His father, Jor-El, was working on a large ship that could transport his family, and a handful of other survivors, to a safe location. While the physical ship itself was finished, the system required to run it was not. He uploads the unfinished system into the smaller rocket to test it, but as Krypton begins to quake, he realizes there is no time left, and he sends Kal-El off in the ship at the very moment of Krypton's death. 
Superman manages to overpower the Eradicator, as he's cleverly allowed them to be close enough to the sun so that he may absorb it's radiation, boosting his powers. He tells Eradicator, "I'm not driven by who I was, or what I could have been, but by who I am, and what I can still be." Superman, using all of his strength, grabs Eradicator, and divebombs with him all the way to Earth. 
As the two of them streak across the sky, and the music builds to it's peak, the people of the world watch in amazement. 
"Look, up in the sky...it's a bird..." 
"It's a plane!" 
"No...it's Superman," says an astonished Lois Lane. 
The atmospheric re-entry burns Eradicator up, and fries his entire system. The impact makes a small crater in the Arctic, but the Eradicator is now totally destroyed. The mechanical plant creatures die, and decay just as quickly as they grew. 
Superman returns to Metropolis, and the entire world cheers for him. At the end of the film, Superman finally agrees to that interview, but before they can start, he flies away to save someone in trouble. 
End credits. 
After the credits, we're taken to a laboratory owned by LexCorp. One of the plant creatures is being autopsied, and Lex is told by a scientist that with this, it may be possible to grow bio-mechanical living tissue. Lex isn't interested until he's told that a sample of Superman's blood was obtained from the scene as well. 
A bit long, but you get the idea. I'm sure there's plenty of room for improvement, but this was just a broad, general idea of a Superman film I'd like to see. As time goes on, I'll likely add to this idea, with things like casting, music, even design