It's probably a lot more expensive than the other schools people are talking about, but you could also do the Skip Barber MX-5 Cup racing school if there's a close location.

It's 3 days, and mechanics take care of the cars so you concentrate on driving more than anything else. Plus it's their cars, so if you smash one into a wall you're only out $200 depending upon if you get extra "vehicle" insurance. Once you're done with the school it also qualifies you for your SCCA regional comp license if you can get a compliance letter from them.

It doesn't teach trackside basics though if that's important too you. Not being your own car might also be a disadvantage depending upon how you look at it. If nothing else, take your car to a solo/autocross event, you'll definitely get the feel for how your car handles. You do have different setups for road race and autocross, but if you want to know what happens when your car is "pushed" you'll definitely find out. It will also help you with recovery techniques.

I didn't have a car at the time, so that's the route I took. There are many options though as others are saying...