You're going to be seriously limiting your options with your $100 price cap. You have a world-class sports car there. Do you really want to handicap the performance by running crappy tires on it? Because in the end, those 4 patches of rubber on the road are the ultimate limiting factor to your acceleration, braking, and handling.
There are a lot of great tires available in that size that you could choose from, but very few of them are under $100 per tire. Contenders I'd be considering for summer tires would be:
Bridgestone Potenza S-03 ($199)
Goodyear Eagle G1 GS-D3 ($165)
Kumho Ecsta MX ($136)
Michelin Pilot Sport PS2 ($183)
Pirelli PZero Rosso ($146)
Bridgestone Potenza RE750 ($156)
For all-season tires, you're probably looking at stuff more like:
Michelin Pilot Sport A/S ($191)
Pirelli PZero Nero M&S ($131)
Sumitomm HTR+ ($83)
Brodgestone Potenza RE950 $(155)
There are loads of others available, too. Check out Tire Rack and Discount Tire, read all the reviews, and then pick something that complements the performance of your car, not necessarily just the cheapest sneakers you can find.