Hero. Think Cloud.
Hero's Love Interest. Think Tifa.
Big Tough Guy. Think Barrett.
Intelligent Guy. Think Balthier.
Happy Guy. Think Zell/Wakka.
Happy Girl. Think Selphie/Rikku/etc.
Mature Girl. Think Quistis/Lulu.
Non-Human Character #1 (Animal based). Think Red XIII.
Non-Human Character #2 (Tiny, tiny humanoid or animal based creature). Because they never do this! Think, like, a hand-sized character. I think it'd be a neat change.
Dark Mysterious Loner Guy. Think Shadow, Vincent, or one of those guys with a bad past from all those Anime shows. You know.
Amusing Psycho Guy. Think Wyllius.
Amusing Weirdo Guy. Think Nait.

EDIT: With regards to classes, you know what would be awesome? Being able to pick a class for every player at the start, and having to finish off with that class. Maybe there would be some point well into the game, maybe two thirds in, where you could change class by going somewhere. But preferrably not. You pick the class, you keep it - just like in FF1 (I think it was that one, anyway). It would make the replayability of the game massive. They could even have the storyline change slightly depending on what class you pick for each player! Endless hours of entertainment! That would be cool. But it would never happen.