Check on your car before hand:
Loose components in engine bay
Lug Nuts
Shake your wheels to check for any sign of play on the wheel for wheel bearing issues
Items to bring:
Extra Oil, Power Steering Fluid
Water/Fluids
Sunscreen (you will get roasted if you don't)
Rain gear (you will get wet if you don't)
Hat/Sunglasses
Chalk (I'll explain)
Ziplock bags to store loose items from your car
Air pressure gauge
Torque Wrench
Typically, as a beginner please run what you currently have. It may be frustrating that your tires may not be the ideal ones, but it will be a valuable learning tool. Throwing on sticker tires will hide your errors and make you slower. I've seen it too many times.
Focus on the nut behind the wheel, you. Learn the lines, push the car. You do not know the limits of the car (and how to correct it) until you exceed. IMO, try and push the car into a spin. Once you do that, you'll know what it feels like and can play with that limit.
IMO - Starting autox is alot easier to do (don't need to worry as much as brake pad life/rotor, tires..etc). In addition, spinning in the middle of a parking lot is much different than a track.
However, the experience is completely different on a track. You cannot compare the two.
When I did my first track day, it was soaking wet. The car was very loose, and there was corrections needed about every turn getting onto power. The instructor said I have probably one of the fastest hands he's seen in a while...and IMO it was contributed to autox...catching skids when you pushed that limit.
Check with your insurance provider, but I know I'm actually covered under HPDEs because it is classified as driver education, and not timed.
Your local chapters should have websites to register for events. Go onto SCCA main page and it can locate your region.
Very basic, but let me know if you need more info