RX8 is a good grip car (4th fastest car in game) and cheap. 911 Turbo is 3rd fastest, gives the most points but an all stage 3 911 Turbo will cost $326,650.
Chager R/T is good for drag (7.5 second 1/4 mile), and later become a great wheelie car.
The 240SX is ok for drift, just does them slowly, but it makes them a bit easier. RX7 is better, but you'll win one of these later on.
I created a career walkthough thread, with suggested cars and setups, plus you can just read or download a text version of it from here:
LinkAlthough I listest the "best" or "best + cheap" car to use, a lot of other, slower cars are still fast enough to win career with.