Well, this is something you have to think about. If you go to a BMW or Porsche club sponsored event (probably other makes too) you will always have an instructor in the car with you.
You are unlikely to find any regular insurance that will provide track coverage, and I've always operated on the assumption that you have no coverage at any kind of track event. Some people suggest you take off your license plates and tape over your vin, but if you do this and have a claim (i.e. "I crashed on the street"), basically you are committing fraud. Evidently you can find some track insurance but it is supposedly very expensive.
Yes, you should be careful as you'll find that many of the "offs" occur in the first session of the day. Unfortunately, even expert drivers can have bad luck. You probably will go off if the car in front of you loses oil or radiator fluid on the track at a critical section and you are the next car to approach.
Another type of event that is much safer on the equipment you might try is an autocross. This is how I started but once you switch over to high speed track events it's hard to go back.
If you car is financed and it's totaled, at a track event, are you prepared to pay until the loan is all paid off but you no longer have the car? Something to think about. You might also try some driver education events where they provide the cars (Audi, Porsche, BMW, Skip Barber and others), until you have enough experience to feel "safe" but it will never be without risk.