Unlocking all of the basic colors and taunts for a character involves picking them at the character select screen at least 17 times. If you're also going after the C to Shining C achievement you'll be getting this and the Fashion Plate achievement naturally, but if you have that achievement grandfathered in from doing it in a previous release of the game you'll have to start again from scratch. You can check your progress per-character by going to Player Data > Character Records and checking the "Number of Times Used" readout; if it's under 17 you have more to unlock.
Easiest way to grind this out is to do a local versus match and quit to menu immediately when the match starts (as unfortunately picking "rematch" locally doesn't increment the counter). You'll need to either manually keep track of how many you have left for each or just move to the next character when you don't have the new taunt/color pop-up when you return to the main menu.