Basically Soap tries to balance "effective racing" with "being a douche who can knock you off the track."

I use Train because of its max acceleration, extremely tight handling, and long MT stat. I use wood instead of roller for their better offroad, plus my use of a featherweight character and Paraglider means I get the highest possible acceleration anyway.
You can use a time trial kart combination, but it's a gamble that you can get to first place, hold it, and hope not many blue shells come along. Time trial karts use one of the top speed frames (usually BDasher, but sometimes Zucchini, Blue 7, and Bruiser) with either slick, red, mushroom, or gold wheels. Slick/gold have the best speed, slicks have better handling/MTs, gold have slightly better offroad/underwater, reds are best offroad (which includes snowy/rainy tracks), and mushrooms have better handling.
Woods are like mini reds, rollers are like mini mushrooms, sponges are like mini slicks.