This one might seem a little silly until you get on the track. I really want to know when you're slowing down. I would love to see when you're starting to brake. On a lot of tracks, you'll be slowing from 140 mph to below 45 mph. It's a good idea to make sure the driver behind knows you intend to slow down rather quickly. It only takes a few sec-onds to check the operation of your brake lights.
Steering And Suspension
Here we're talking about excessive play in the steering components. You should put the car up on jackstands and check to see that the tie-rod ends are in good condition. You can also check for bearing play while the car is up in the air. I prefer to check my own tie rods rather than have a shop do it, but you may have found a shop you trust.
You should also consider using synthetic power-steering fluid, as it mitigates any possible heat breakdown. It also withstands severe temperatures much better than conventional fluid. The other thing is that, at the track, the steering will work much harder than it might on the street. You're going to create a lot of heat while on the track.
Don't worry about this for your first few track days, but as you continue to track your car, using a better synthetic power-steering fluid should be on your list of upgrades.
What About Tires?
Tires are a big deal. In the beginning, though, you just need to have decent tires on your Corvette. Your regular street tires are fine for your first few track events. Don't get overly concerned about having the latest DOT-approved track tires. You're not ready for that step yet. Don't even think about buying new tires until you've completed a few events.
Tires are the great divide. There are street tires and there are single-purpose DOT-approved tires that really shouldn't be driven on the street. Kumho and Hoosier both make tires for your Corvette that are incredible on the track, as they will stick to dry pavement extremely well. They also wear incredibly fast, and you shouldn't even think about using them in wet weather. Once you make the decision to use DOT tires, you've crossed over the line into a whole new world. The problem is you can't drive any real distance on the DOT track tires, and the ride quality is non-existent. Take a look at the Kumho and Hoosier tires on some of the cars at the track and then think about being on the expressway during a rainstorm. It's not pretty.
It's not just a matter of buying DOT tires, though. Since you can't use these DOT single-purpose tires during the week, you're going to need a new set of wheels. Now you have to get this extra set of wheels to the track and back. Did you really intend to buy a truck and trailer for your weekend fun? It's a long, slippery slope once you get really serious. Don't start down that slope unless you have extra money in your home-equity account.
Don't Screw With The Car
The main rule for having fun is to not screw with the car. Run the thing stock. The problem isn't with your Corvette. The problem is with the way you drive. During the first year, and maybe for a few more years, your Corvette will be faster than you are. Spend money on entering more events, not on a bunch of things that won't make you any faster. Too many people get excited about messing with the car and forget that they're the main factor in whether or not the car is fast. I see guys on the Internet forums asking which exhaust system they should purchase for their first track event. Give me a break. It's really all about driving. You shouldn't start making changes until you know that you're a decent driver. You'll know when that time arrives. If you really feel the need to spend money, you might want to hire a driving coach. That investment will probably do more for your lap times than any modification you might add to the car.