I was in your shoes about this time last year. I had a friend who was an instructor in the BMW CCA. They have 'skid schools' to prepare people for their first day on the track. It had smoking donut exercises on a skid pad (with hoses to reduce the smoking), a mini-autocross, and braking exercises. I sucked at the braking, btw. It was a blast, and very inexpensive.
Then I signed up for my first track day with that club. They had great support for first-timers, were very welcoming to non-Bimmer drivers, and in general were a really nice bunch of people who put together a great event. I've since become addicted and have made it to a bunch of tracks, and gotten to know a whole new crowd of people. See if there are car clubs in your area that arrange track days. There's a continuity there that you might not find if you go to a race school, and you might get better prepared to learn more advanced skills should you choose to do an expensive race school later. I liked the BMW CCA, but there may be better ones in your area.
MotorsportReg.com : MotorsportReg.com > Online registration management tools for driving and social events has a lot of events which you could check out. I highly recommend the skid school first (BMWCCA calls it Advanced Driving Skills School).