Well, your parents are probably right in this case. They aren't really a practical car for someone just starting out, especially if you don't have the means (read: disposable income) to spend on the car to fix whatever problems it's got once you've bought it. And those problems will be there, without a doubt.
Put a MkIII down on your to-do list, right alongside that cute red-head in your lit class.
Once you're in a better position to burn money regularly, then go for the Supra. Trust us, they're more jealous of your time and money than the most high-maintenance girlfriend you can possibly imagine.