There are a lot of car clubs that organize "Track Days". My son and I belong to the local Mercedes Club (but don't own a Mercedes). We joined years ago in order to run in their track events (autocross and various tracks). My son also is a member of the SVT organization as well. They run lots of track events, but few or no autocross events. Track events will usually cost anywhere from$160 to $200 per day at the track.
Autocross is actually competition, of course, but running against a clock, one car at a time. The track events are more of a driving school with no passing in turns, etc. Each club will have their own rules - the Mercedes Club breaks it down into 'groups" based on experience and has instructors for each novice.
But do try this out. You will find that you will become a much better driver as a result of participating in autocross and track events.
Good luck to you!!
Harry
PS: the Mercedes Club web site is:
www.gws-mbca.org