Check out this thread. It shows a member's journey through the game using the least amount of credits and cars necessary to complete the game. It's also a terrific read as well!!
Buy a Vitz. As aforementioned, you win most of the other good ones and it'll come in handy for the Vitz race, I tell you - because the Sunday Cup ones aren't brilliant at winning it for you.
Although I started with a Civic, but I had the Stealth Models from the start. Didn't find the Chrome Lines till much later on
I started the game out with a Toyota Corolla Levin BZR '98. It was in the UCD and had 171 hp after an oil change, if I recall. It cost somewhere in the 15,000 range, so there was money left over to do performance upgrades as well.