These are the cars I went with.

** After reach #2 in the world, I've got an update to this post.   See Post #5 below

A1 - 370Z.  This is your starter car, if you turn off asssits you don't need to upgrade this car very much to win the races. 
A2 - Z4 Roadster 
A3 - Alfa 4C

(For A series, speed tracks are better with the 4C, while curvy tracks are for the Z4)

B1 - M4 Coupe
B2 - Alfa 8C
B3 - M6 Coupe 

(For the B series, the M6 is a beast, upgrade this car as this car will win you a lot of multiplayer races)

C1 - NSX
C2 - 12C

D1 - P1.  

The P1 is fast, and there is debate whether it's the best car here.  The driving style for this car is totally different than all the other cars in this game.   It requires you to stay on track and not hit any barriers to win, you need to harness your RR3 driving style for this car.  The RUF can be driven more agressively to achieve good times.