In keeping it on topic yet dousing the flames, a new driver would be smart to make sure they are not -excluded- from coverage for any damages at a track. Policies are worded cleverly nowadays such that even autocross is considered "racing."
A new driver would also do themselves well to find a reputable event sponsor to sign on with. I've been fortunate to have driven with a variety of very well organized groups with extremely low tolerance for uninvited passing nor vehicles unfit for track driving. If you're reading along and this discussion on liability and unsafe conditions frightens you, it should. Not a one of us here is interested in leaving our cars at the track in a wad or series of small chunks. We're not afraid of it, but we're also not driving so carelessly that we'd cause it to happen.
We're very in tune with our cars; the noises they make, the vibrations they produce, smells, attitudes, even what some parts taste like. This stuff didn't just magically appear in our psyche but it grew there through experience, time, talking to other drivers, and yes, sometimes having stuff break.
Fear of the unknown is a perfectly natural thing. In fact, I just sent in an editorial to 'vortex for consideration all about fear and why it ought not keep any driver away from higher driver training. Allowing fear to keep us from moving forward is what isn't healthy. Fear of the track, fear of the insurance man, fear of not being ready, fear of being the new guy who's really slow... nonsense. Face your fears with just a little bravery and you'll see there isn't much to be scared of afterall. Not even the insurance man.
Heck, you might find your insurance company will give you a discount for completing some schools like accident avoidance or winter driving.
I recommend looking for experienced drivers near you too whom have been there and done that. They started out where you are now and often a face to face over a coffee does more than reading some entusiastic strangers on an Internet forum.