Superman stories should be about Superman being super. Most folks want to make it about other people being around Superman, but that's just not as good a take. It doesn't really work for any fictional character if you think about it. We want to see them doing what they do. All the supporting cast should be there to advance the plot or spur the character, but nothing more than that. It's got to be about Superman.
I agree completely on Mark's take and the triangle. Superman is the real character, able to do anything. He's a caretaker for Earth but he can never fit in. He can't really be best buddies with Batman, he shouldn't have other heroes in the same league as him. Others should be able to one thing he can do (like the Flash can race him) but he would blow them away in any other skill. Clark is Superman wearing a fake beard, pretending to fit in, but Clark doesn't really exist.
I've always felt Batman rose as a character on the back of Superman falling. So few people recognized that Superman threw their fight in Dark Knight, instead they saw it as Batman (the billionaire) fighting against the all power Man (the poor farm kid). It's funny, I think fans respond better to heroes who 'earned' their powers rather than admire those born with gifts. It's an interesting fictional dynamic.
Lois should be more driven, committed and lonely than any other character. She's sacrificed everything to get where she is, and Superman sees that. He sees her strength in being alone and admires her in choosing it. He can't love her, but in his pretend role as Clark he can. He's as good a person he can be for her, but she can't really be with him, so he's content in her not loving him back. Their relationship is really beautiful, and one of the things the Reeve movies got right.
Luthor should be the greatest leader of humanity, the smartest guy who would lead the planet to a golden age. Except he can't stand that Superman is there instead, and it's corrupted his mind.