Technically everything between gettin the airship in the WoR and Kefka's Tower is a sidequest. You can finish the game with just Celes, Edgar and Setzer (you have to beef 'em up proper, though).
Done it. (See, that's what you get when you cross an excellent game with a guy who had absolutely no life at the time.)

Damn Papa. It's rigged! I kept trying to buy the Chocobo, which if I remember correctly is only half a million, and they wouldn't let me bid again.