Definitely start with at least one CCA car control clinic. Then you can sign up for lapping days. I have attended 2 car control clinics and 2 sessions at the track. The learning curve is steep so I would get some skills down prior to spending the $3000.
The car control clinics have a class associated with them. They will inform you that to do heel and toe you need to practice in every day driving for a long time before it would make sense to try it on the track. You certainly don't won't to be concentrating on that with the myriad of other things on your mind.
As far as beating up your car goes, I guess I could argue that either way. But why own these cars if we can't use them occasionally. My track day last Weds use about 1/5 of my tires, so that could get expensive. But it is a hell of a lot of fun and you don't have to be the best to enjoy it.
2015 f80 M3, 2016 GT3