I was thinking "cheap" rental car. I autocrossed a Hyunai Elantra a few weeks ago. Not fast, but fun enough once I figured out how to drive it. (which amounted to "drive it like you stole it" with very high tire pressures) That car cost me $46... for THREE days! It was $13/day.
Any of the "fun" cars will cost way more to rent. And, I'll warn you, things like the Shelby are monitored. You might get away with an autocross, but if you drive obscene speeds on the highway, or especially if you take it to a race track... they'll know.
One of the clubs I used to be in did an "IROC" challenge autocross once. Something like 12 drivers. One rented Dodge Neon.