I participated in a series called Evolution
http://autocross.com/evolution/
THey basically cover 99% of what you will learn in a MUCH MORE expensive driving school like Skip Barber, Bondurant etc. but the cost is only a fraction since you are driving your own car and not helping to fund a fleet of cars of differing categories.
Your car will take some abuse mostly depending on the type of course and the surface. This type of driving is not all like anything you'll do on the open road.
If you plan to Autocross regularly next season you might want to upgrade your brake pads and have a spare set of tires and wheels to drive to events. THis car is only a weekend driver for me so I decided with the street legal R compounds from Toyo rather than to change the set up for events. I'll have to ditch those tires soon as the winter temps approach.
oh and did it improve my driving?
You'll realize how many mistakes you have been making your whole driving life. It also had the side effect of making me a terrible passenger I almost have to be blind folded and gagged when my lady friend is driving her car at high speeds.
I now avoid major highways full of SUV's and stick to the local roads whenever possible. SOme people should not be allowed to drive.