For me, I mainly use these characters for most races.
Character: Dry Bones
Kart: Don't use them
Bike: Bullet Bike
Always Manuel
The bullet bike is an excellent bike with a very high speed, mini-turbo and drift stat. Overall, it's a very fast bike.
Character: Yoshi
Kart: Don't use
Bike: Mach Bike
Always Manuel
The Mach Bike has very similar stats to the bullet bike. The bullet has slighty better acceleration, drift, and miniturbo, but the Mach Bike makes it up for its increased weight. Whenever I'm in a Grand Prix, and I get too bumped around, and switch to the Mach Bike, and it's a bit more stable.
These bikes both have IN drift, you have to get used to them for a while before you can actually benefit from them. It's worth it though, these two bikes are the renowned speed bikes. For characters, there are some very miniscule stat changes, but they don't make much of a difference, so feel free to choose whoever you want.