TLDR: Drive your own car. You're unlikely to have $900 worth of wear for a novice autocross day.
I've done BMW CCA Boston chapter Advanced Car Control Clinic (AC3) at Lime Rock on the lime rock infield. It's not exactly the same thing as what you're signed up for, but I imagine it will be run similarly. They'll basically send you out maybe 3-4 cars at a time, with a decent gap between cars, and you'll run the infield course on some configuration. It's not racing, and if you catch the car in front, you should be slowing down to build another gap. It's also not traditional autocross where you run the course once, and then come in. It's meant for you to have some more seat time learning the characteristics of your car. It feels different to autocross as well, as you can have some 'rhythm' from lapping, like you would on the full track.
They will design the course so that you will never exceed 2nd gear speeds. It will be possible for you to lose control of your car, but be safe and get the car slowed down. With autocross, generally the only things you'll hit are cones. The lime rock infield does have some pretty far off trees, and there's a gazebo that's a fair bit off the course. It is possible to run into those, but only with 'target fixation'. Slowly work up to your own comfort level and you'll be fine.
The front undertray for our cars are felt, and they don't hold up too too well to cones, but they can take a few hits. Mine was chewed up by the original owner a bit from low driveways, and I think I did 3 driving school events where I hit plenty of cones before it got chewed up enough that I decided to replace it. You'll have some very minor wear from stressing your tires, suspension components, cooling system, etc more so than street miles, but it won't be significant or measurable really.
Mostly, the experience of pushing your own car is valuable for extenuating circumstances on the road. Bring your own car
