Without a doubt, Lex Luthor and Brainiac. I'd say the first film should take some of the plot from Geoff Johns' recent Brainiac arc, some of the sentiment from All Star Superman, and top it off with a few ideas from Lex Luthor: Man of Steel.
Have Brainiac be the Big Bad. Perhaps do what Johns did, and tie Brainiac into the destruction of Krypton: that'd make for a great opening sequence. Then skip through all the origin stuff in montage - perhaps over the opening credits - and have the main story set in a world where Superman is well established, Clark Kent works at the Daily Planet with Lois Lane and the rest of the ensemble, and Lex Luthor as the mad scientist villain he was in the Silver Age/has somewhat reverted to in the current comics. No Donner Luthor, please.
Have the main thrust of the plot be that Brainiac has targeted Earth as his next target for destruction, in the vein of what he did to Krypton. But first, his drones attack Earth, go for a full-on alien invasion idea. This allows Lex Luthor to paint himself as a "hero of the people" of sorts, saying that humanity needs to unite against the alien outsiders, and trying to turn people against Superman. Perhaps have Luthor start working with the military in some campaign against Brainiac's forces, which goes disastrously wrong.
I actually imagine a scenario for the film's conclusion where we have Superman and Lex Luthor in his powersuit reluctantly joining forces as the two of them infiltrate Brainiac's mothership in an attempt to stop his conquest of Earth. But after the day is saved, Luthor manages to claim most of the credit for himself, and becomes beloved by Metropolis, setting the groundwork for Lexcorp to be formed in the sequel. Though I'd also be okay with Lexcorp Lex being established in the first film rather than him starting as a mad scientist and transitioning into running Lexcorp.
As for the sequel, if they get that far, I'd love to see some variation on The Everyman Project from 52. It's hard to think of a masterplan by Lex Luthor that's been more callous. Also through another villain like Parasite or Metallo into the mix.