That is WWWWWWWAAAAAAAAAYYYYYYYYY!!!!!!!! too much money for a modified Supra. WAY too much. Modified cars are generally unreliable, no matter what quality of work was done and obviously they've been driven very hard. If you want a Supra, get a low-milage, unmodified, late-model car. You'll have less problems with it. Generally it'll have been used as a weekend car and not driven as hard.
Now, as for alternatives. When you say "race," what exactly do you mean by that? There are many forms of amateur racing out there: drag racing, autocross, road course, just to name a few. I suppose there's also street racing. But if that's what you're talking about, then I'll just slide out of this thread entirely.
If you're in the market for a car to focus on one racing style, make sure the car fits that type of racing. Also factor in how often you'll be racing it vs daily driving it.
If you want to autocross, then light weight is your friend. So is a small car. Excellent choices for autocross include miatas, integras, neons (don't bother with the SRT-4, i'd go for an older ACR package), Probes, and Saturn SC2's.
If wider-open road courses are your thing, then you bring out the bigger guns. Corvettes, Vipers, Supras, RX-7s, STi, Evo, BMW M3. Find a balanced chassis, a powerful motor, and rear- or all-wheel drive. In lighter classes, the aforementioned autocross cars are all competitive.
Just wanna go really fast? Drag racing. Two words for you. American Muscle. The only things that matter are traction, power, and driver. For traction, you'll need lots of tire and rear- or all-wheel drive. Front-drive cars are really just a waste of time unless you're one of those people who feels the need to prove something. Power needs to be predictable, strong, and broad. Peaky motors need not apply. Big american V8's dominate. They make huge power out of the box and it just gets better with mods. If you rock at driving, get a manual trans. If you suck, get an automatic. Just remember if you want to compete, the key is consistency, not speed.