This is more for die hard people since this one is hard to get to work. GP2 has like 95+% of everything GP1 has so if your only interested in getting one mario game, I recommend you choose GP2 and follow the link above. This is how to get Mario Kart GP1 to work.
UPDATE: you can also play GP2 using this method but the link above is still the easiest way to play GP2 I have previously posted how to play Mario Kart GP2 on Dolphin Triforce 3.0-694.