Personally, I tend to like Light Karts the best, I'm not sure why, but I use them a lot. I guess it's because I like how the bullet bike works and I used them a lot in Mario Kart DS.
Advantages: Tend to have more off road and acceleration than other karts, Bullet Bike has the hardest drifting in the game, and the stats help when trying to recover from a hit.
Disadvantages: Tend to have less speed and weight than other karts, get pushed off by heavy karts a lot, and off road doesn't help THAT much