I would agree with both comments above. Work your way into the sport, talk to other drivers at events and find out what they are using and what works for them. Me, I have been very impressed with the Michelin Pilot Sport PS2 on my boxster right now.
I autocross a miata most of the time, I started out on street tires and then graduated to r-comp tires and it is a real blast, I occasionally autocross the boxster when the local PCA has events and the level of grip the PS2's provide is pretty amazing imo.
If you are considering a second set of wheels with r-compound tires for autocross, have a look at the Kumho VictoRacer V700 or the Escta V710. Both are very popular autocross tires.
If you are looking for "double duty" autocross + street tires, have a look at the Michelin Pilot sport PS2, Bridgestone Potenza RE-01R, Hankook Ventus RS2, or the Falken Azenis 615. I have had good experiences with each of those tires.
If you didn't make it out to todays PCA autocross event, the next one is Sunday April 6, hope to see you there!
