The rules state that a helmut is required for anything 13.99 or faster. That said, the track I go to requires a helmet for everyone, including a bone stock beetle that runs 20.x at 60mph. The helmet should be Snell SA, not M (motorcycle) and some tracks may be picky about that. Other tracks don't care at all if you wear a helmet, but I haven't been to one of those.
A firejacket is typically required for anyone 11.99 or faster or anyone that has a power adder (blower, turbo, nitrous). However, for cars with a stock turbo or stock blower, they won't ussually require it. I got in trouble for not having a firejacket on my 2.3 with a stock turbo running high 12s. I guess they thought I was pushing that rule too far.
Typical insurance will not cover you on the track, however there are some specialty policys of sorts that you can get from some companies that will cover you. It is much more common to find this type of insurance for a road course though.
When I go to the track, I typically bring my small cigarette lighter powered air compressor, tire gauge, box of tools, nitrous bottle, fire jacket, helmet, box of random spare parts, camera and water. But that's for my 88, it is slightly less than reliable.
In the 97, ussually just my helmet, and water to drink. I don't bring coolant... they have places to get water and plain water will work just fine to get you home.