Welcome, and no worries about not having a BMW. You can have fun in any car. Lots of people come in Corollas, Impalas, Minis, Integras, etc.
Autocross and tracking mostly just wear out your tires and brakes quicker. If you're smooth, it won't be much at all.
You will also stress your engine/drivetrain more than normal, so more frequent engine, transmission, differential oil, etc. are recommended (you should be doing this on a street only car as well, factory recommendations only care to get the car out of warranty)
You'll just want to make sure your car is in good mechanical condition.
Of course, the real cost is once you get hooked. You'll want upgraded tires, brakes, suspension, etc.
I would recommend BMW Trillium's driving schools as a good place to start.
Autocross/autoslalom is also a great way to get a feel for your car at slower speeds in a safe environment.