BTW, I mention the 787B because it probably handles better than anything except the F1 cars.
The popular thing for people who don't want a challenge is to buy an OK car then go win the Super Speedway Endurance until you get the F090/S. It's easy to win with any car with 500 HP.
The best car you can win the easiest is the Camaro Race Car you get from the Amateur American Championship. The Camaro can win any race it can enter short of the Formula GT, and the American Championship is easy enough that it is very possible to win with the first car you bought. I've won the American Championship series with the Trueno and with the Miata, but a new player probably couldn't catch the Corvette C5R. It should be easy with anything over 400 HP, though. The series is just really easy. It's just five 3-lap races, there's no tire wear, and the best competition is some Corvettes.
There's no point in buying a car and getting it up to more than 500 HP, because by that time you'll be able to win something much better. You really just need a car with 400-500 HP to win the car you want. Good ones that handle pretty well and don't weigh too much are:
Lancer Evo VI RS: $25,980, 563 max HP
MR2 GT-S: $27,130, 506 max HP
S2000, $33,800, 544 max HP
RX-7 Type RZ: $39,980, 655 max HP
Corvette Z06: $54,000, 786 max HP
TVR Tuscan: $80,780, 655 max HP
The Lancer doesn't handle quite as well as the other ones, but it's a really good deal.
The MR2 and S2000 are pretty good all around, but only have 250 HP without upgrades.
The RX-7 is fast and handles really well, but maybe a little slower getting up to speed.
The Corvette is the best one, but it's also the heaviest, and really overkill for an early car to buy.
The Tuscan is a good car to get, because it's the only car in the game that you absolutely have to buy to complete the game. It's also extremely light and comes stock with 350 HP.
The WRX and some of the other Evo's are pretty good, too.