There is no single "best" vehicle in any class, but there are generally only two or three at the top of each list. I suggest test driving each car by doing solo races before buying since it can be a very costly mistake (when you sell vehicles you've purchased, you'll only receive half the value of the car plus half the value of any installed mods and paint jobs. This works out to about a $625,000 loss on a fully modded Adder, the most expensive vehicle in the game, excluding Pegasus vehicles).
Super: The Adder has the highest speed, the Zentorno has the best acceleration (excluding the Voltic, which is an electric vehicle and has an extremely low top speed for a super car), and the Entity is in between with better acceleration than the Adder and better speed than the Zentorno.
Sports: Most people prefer the Elegy RH8 (which is free to purchase if you're a R* Social Club member, but you can't sell it). I think the RH8 has awful braking, and prefer the Massacro, which has good acceleration, speed, and handling. The Rapid GT has phenomenal acceleration, one of the best in the game regardless of class.
Motorbikes: The Hakuchou is the fastest and the Bati has the best acceleration. Avoid any choppers, like the Innovation or the Daemon, they can't make sharp turns, and acceleration is typically lower than the others in this class.
Sports Classics: All cars in this class have bad braking and handling, and require some skill to use drive them well. The Coquette Classic is fast, but has the (among) worst handling. I prefer the Monroe, it has better handling than others, as well as good speed and (one of) the highest acceleration. Stay away from the Tornado, it has very low speed and low acceleration.
Muscle: I use the Gauntlet and Dominator, but there really is no wrong car here. Most muscle cars exhibit the same problem of spinning out on turns, so they take some practice. The Ruiner, for whatever reason, seems to be less prone to this problem (I could be wrong, I rarely use it).
SUV: The Huntley S is fantastic. Having said that, I haven't really driven any other SUVs.
Compact: They're all pretty bad. I hate the Blista the least, but have seen amazing performances in the Panto by skilled drivers. Skip the Issi, it can't climb worth a damn.
Sedan: Your call. You might consider the Super Diamond, which was originally classified as a Sports car.
Coupe: I used to use the F620, which was ok, but now use the Exemplar. It's a 4-door version of the Rapid GT sports car. I've only used it in one or two races, but haven't had any issues with it.
Off Road: I typically recommend the Sanchez. It can maneuver in ways cars and trucks can, but the Injection is faster and better for races with long stretches. I can't recommend any ATVs as I've never used them. The Enduro is a fun bike, but won't win you any races, unless they involve climbing 80 degree slopes. Don't buy the Merryweather Mesa if you're not sure if you'll keep it; you can't sell it back (if this has been patched, please correct me).
Hope this helps, if you have any more questions feel free to message me.