I would do a complete reboot, like Batman Begins and Bond.
However, I would not give the origin story as the main story, but do it like The Hulk and have the origin (from Reeve's film) told through the opening credits.
For the story itself, I would have a real hard-hitting story, like Superman facing off against Luthor as the latter tries to get into the White House through nefarious means that only our hero knows about. Of course no one believes Superman and he is forced to officially hang up his cape as Luthor becomes US President - it's not always a happy ending.
The sequel would have Superman deciding to screw orders and reveal the devious bastard's schemes, letting the people remove Luthor from office, with Superman's help.