I'm with LD and Fifth, but I do take stats into account and try out the different characters to get a feel for who I'm best with. With the Mario Karts games, though, I already have an idea of what stats I'm best with: karts with high acceleration. I value that higher than top speed, tracking, weight, etc. Since I can't have good "everything," I like decent tracking/drift (not Peach), not horrible top-speed (not Dry Bones), and decent items. Weight doesn't really play much of a factor in my decision, but I prefer to not have a really light weight. Yoshi in the Cucumber fits most with what I prefer, so that's who and what I choose--and am best with.
I've consistently been best with Yoshi in all the Mario Karts except Double Dash!!.
Pretty much, I'll compromise top-speed for acceleration and weight for items. The rest is fine in the middle.