Whilst the other guide is a decent way to get the achievement you can also do it this way
You can just purchase any of these 5 cheap cars, to help you along the way.
Nissian 240SX (S13) - $20,000 (Japanese)
Mazda RX-8 - $22,000 (Japanese)
Pontiac Solstice GXP - $25,000 (American)
Nissian Silvia (S15) - $28,000 (Japanese)
Pontiac GTO - $32,000 (American)