High Performance Driver Education or HPDE events are a great way to get out on the track.
There are many, many clubs that have these types of events and most break up their sessions into groups based on experience level. Usually this means Novice (with instructors in the car with limited point-by passing only), Intermediate (with instructors in the car at many clubs and usually point by passing is allowed in a greater number of areas), and Advanced (no instructor and, depending on the club, liberal passing zones and with or without point-by). Many clubs require you to run Novice regardless of your past experience, unless you come proof like your competition license or log book. But don't worry, they just want to make sure you're safe before releasing you to the other groups. HPDE's are all about safety, learning, and, of course, having fun.
For most clubs, you'll start off in the classroom to learn some basics and the rules to follow when running with that club (pay close attention because some clubs do things differently). Then you'll hit the track for what is usually 45 minutes to an hour for each of the groups. Make sure you plan for lunch, fuel, and have a few spare parts (particularly brake pads for the more challenging tracks).
A very large number of tracks are available but almost all are road course venues - in fact, I have yet to see an HPDE on an oval.
In most cases, a helmet and your road car is all you need (some clubs require street registered vehicles) so there is not a lot of extra things you need to buy.
A word of warning though: Not all clubs have vigorous criteria for their instructors. The bare minimum should be an MSF Level 2 Instructor for your in-car instruction and an MSF Level 1 instructor for any classroom instruction.
Another word of warning: These are NOT competitions! These are learning events.
HPDE insurance is available for most events - because your regular insurance will definitely not cover any damage to your vehicle.
Relatively low cost, most are in the $200-300 range for all day
Provides a great place to learn how to handle your car
Quite a bit of track time at a wide-variety of tracks
Low threat (in most cases) so you can learn some while you are on your favorite track
HPDE insurance is available
Not all instructors are created equal
It isn't a competition, so if that's what you're looking for this isn't it
If you are running your daily driver, it can really tax key components which will likely increase your maintenance cost
HPDE insurance can be expensive