I say go with your M3 at the track, it really is the best place to enjoy and appreciate the capabilities of the car. IMO, no need to start with a beater or your Mini.
As many others have said, as a newb, just keep the car stock. You probably won't even need to upgrade the brakes for the first few events. Most definitely stick with street tires for the first few seasons.
If you do get hooked to the sport, you can start looking at mods that will improve safety like better track brake pads.
I am a firm believer that the best component worth modding is the one between the seat and the steering wheel
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And most importantly, HAVE FUN
