There are all sort of excuses. A car is going to cost one or two grand for a decent looking sports car. Keep in mind American cars stopped being worth buying since about 1970, the only cars worth thinking about are Japanese and European, but mainly Nissan and Toyota. Most guys think girls are into luxury cars, or new cars, because this is what they tell you. The fact is, when she's been over 200 mph in your Skyline GTR (this one is worth over 18k, but irregardless), she'll forget how uncomfortable it is and that it's 15 years old.
You can get a stock version of the cars below (Nissan 240SX and Toyota Supra, circa ~1990), with some minor body damage, for a couple thousand dollars. Slowly start working on it and modifying it, and it will look like this. Cheapest and generally the best way to get a nice fast car.
http://www.modifiedstreetcars.com/car_images/nissan/Nissan-S13.5-513.jpg
http://www.autotuning.cz/galerie/albums/userpics/normal_MK%20III%20By%20K_Ss.jpg
As for the parents thing, getting a license isn't expensive, and if you get a job, there's not much they can do to stop you from buying a car. If you can't afford gas, don't use it much.
Oh and by the way: these cars may look like ricers, however, there's an important distinction. True ricers are front wheel drive and have purely cosmetic upgrades. Most Hondas or Acuras that have been "tricked out" are ricers. A RWD Nissan or Toyota is not a ricer. It is a race/drift machine, and for the price, will
easily outperform anything else on the road.