Firstly forget all your anxiety.
Yes show up early the day before and enjoy exploring the facilities. Even if your condo is not ready they will give you a wrist band and direct you to the clubhouse where you can relax inside with a snack and drinks 
of any kind. I enjoyed sitting outside the clubhouse with my drink and watching the club members in various cars roaring around the track. This is the big track and not the one used for the school. You will register with the rest of the folks in the morning at the gift shop. Extra insurance (deductable coverage) will be offered to you then if you are driving a Stingray. Not available for GS and Z06. Thus I did it get it. Not sure how many did but what they told me is only 1 time there was an incident where it would have been relevant anyway. This was not even realated to a driver error. (Medical condition caused the guy to leave the track apparently).
And yes you will be given a car with your exact configuration and the transmission will be what you own. They have your vin so it’s all prearranged. They will tell you your car #.
Ok age and expectations.
There are guys in this course from 20s to 80s. Most 45-70s. In my class we had an elderly guy (veteran) with 1 leg. He got to his car in a power chair. He did great and the comradary develops very quick in the group. Aggressive people or drivers are simply handled by the excellent instructors instantly before anyone gets close to a car. Thus you will likely not see anything like that.
They bring you up to making actual laps with a series of simple driving technique practices. So you get to drive the car and get more relaxed and comfortable doing some specific stuff before any laps are done. So some events have an instructor in the car with you, and the track time you are following the instructor. You set the pace and he is coaching you. Good luck trying to catch him if you think you can 
You have a radio in your car and are receiving personal instruction, praise and advice every moment you are in the car. I’m not kidding; they call you by your first name. Incredibly positive and you feel these guys are on your side. They want you to enjoy your experience and do well. You will be very impressed with this particular aspect of the experience.
There is a series of events with the cars that give you experience with the antilock brakes, stability control and basic technique on how to drive the car around a course. Where and when you should be looking for example. Again no pressure, positive and a great deal of fun.
They will be breaking the class up into 2 main groups. One in cars and one in the classroom at all time. So all the things you do in the car will be explained in the classroom first.
As you drive your car through the exercises you will be evaluated by the instructors without your knowledge through observation. They will then divide the class up again to groups of 4 or 5 cars that will move around the track together. This puts drivers with similar ability together. It is not uncommon to be promoted to a faster track group and those struggling to keep up will be moved to a slower group. Makes the experience better as nobody is feeling intimidated.
So the best thing to do is pay close attention and make a good effort to focus on using the techniques they teach you. Believe it or not you will become faster and faster. Your confidence of the capabilities of the car will grow and grow along with you own. Don’t worry you will be out of your comfort zone cornering at first but using what they show you that will disappear very quickly. This is not a class on driving around town. You are encouraged to press this car hard but active the handling system is on, so relax. Remember as you are following your instructor he is talking to you the entire lap to help you with technique and give you confidence.
Yes it’s true that I was able to quickly demonstrate (with the instructor in the car for this exercise) that I understood and could handle a full on active handling intervention sliding on the wet skid pad. So I just did donuts after that till my time was up. Guess what; he was laughing his head off and I had a blast.
There is a small oval event you will really enjoy. This comes late in the course after you have had some track time. This I where you really get to learn just how far you can push these cars on a dry track. It was an outstanding experience with the instructor sitting in the right hand seat explaining the corners to you and saying “ok Derek full throttle now”
The track time is even more fun after that. Yes my Z06 car had the back end move a bit but the car sorted it out effortlessly with just basic input from me. Soon this was when I knew I was getting it right. Especially when the instructor was telling me “well done / great corner” etc
You will be a bit sad to see it end as you say farewell to the new friends you just made.
We did just what you are doing with adding a few nights in Vegas. One thing I can tell you... you feel like an F1 champion on your way back to Vegas. I tried gambling in the casino like one and well... that’s another story but it turns out I’m not. Although I sure get a ton of VIP invites back to the Pallazo.
Pardon the long story but for sure you will fit right in and have a great time while getting to legally drive a Corvette as fast as you want. Not many actually get do this and you will see your car in a whole new way after. Yes you will love it even more.
D
PS. Be sure and bring your SD card for the PDR and take advantage of the photographer that offers to capture you on the track. Worth every penny.