On the N64 version, I played Capt. Falcon almost exclusively, followed by Samus.
On the GC, I like playing Doc Mario, Mewtwo, Capt. Falcon, Zelda/Sheik, Samus, the Ice Climbers, Bowser, Young Link, Roy, Peach, and Ganondorf. I'm sort of stuck as to say which is my fave... I use Cap a lot, but I'll pick a character based more on the competition that I'm likely to face than anything else.
Tip: If you play as Mewtwo, use weapons like the star rod, beam sword, and parasol as much as possible. MT is one of the nastiest weapons-weilders in the game, which surprised me.