When on the character selection screen, highlight the wrestler you want to play as. Instead of choosing with X, hit the Start button. I think all the wrestlers have a second outfit, but I'm not sure. Here are a couple:

Hulk Hogan:
Press the Start button to get his old yellow "Hulkamania" duds.

Sting:
Press the Start button to get him with blonde hair and different clothes (his old style).