Nick- it sounds like you want to autocross but are completely lost with regards to rules/classing and the level of involvement you want to have in the sport.

As mentioned by axemansean, the #1 thing for someone entering the sport, is JUST GO PARTICIPATE!!. Allow the people at your local organization to help you, they'll get you into the class most appropriate for you, and guide you through the course a few times. Don't be shy, embarrassed or ashamed of your results, mistakes, or the number of cones you run over. Just drive. I guarantee you'll be hooked.

Tires actually matter very little when you first start out. (I started on Michelin Pilot XGT V4s.) Its figuring out how to drive through those orange-cone-pylon-things that's tough. When you do autocross just make sure you set your tire pressures higher in the front; around 45psi should do fine on stock wheels. You can leave the rear pressures at approximately what you run on the street.

Other than that....HAVE FUN.