I used a street car, on street tires.
2004 Corvette Z06. 610HP - Sports Soft Tires.
I did my best to build the car to match the S2000 specs, but I found myself racing the orange TT because it had a much smarter pit strategy.
The point is though, you definitely don't need a race car, and you definitely don't need race tires. You do need to get 4 laps out of each set of tires though.
I won the race by about 15 seconds over the TT.