It's getting a little late
To explain the complete, and proper sequence of all the necessary steps to complete the job would fill the CAC board this evening, so I will address only the basic procedures.
Normally it is best to sand and buff within the first 24 hours, after the final clear coat has dried. The longer you wait after that, the more difficult it becomes because of the surface, that gets progressively harder, there by making the sand/polish operation much more difficult to accomplish.
As far as recommendations, I would go with the 2000 grit, and stay with a high quality paper such as 3M. This is not a place for the cheapie supplies. You will need an electric buffer, and it is imperative that it be one with a variable speed.
The best pads I ever used were also supplied by 3M and they were not the flat type, but rather those ( check pic ) filled with a pattern of little knobs.
As far as the compound itself, it would be better to inquire at your local auto-parts supply, because most have their own brands, and often they have employees who can recommend the exact products you should be using.
Before starting the sanding procedure, be sure your surface is absolutely spotless, because any dirt that's on the surface will be sanded into your new finish and I promise you , you will not be a happy camper. The regular size sheets of paper should be cut in half and folder in three, before letting a few of them soak in a plastic pail of lukewarm water for at least an hour before use. You also want to be sure to put two to three drops ( no more ) of dish washing detergent in the pail you will be using. The use of the soap will make a world of difference in your sanding.
You will need a small rubber scraper about 2" by 3" and keep it close because as you sand a small section of the surface ( 12" by 12" max ) at a time, you use the scrapper to check the progress. The surface will be ready to buff when the clear has completely lost it's sheen, and become ( after scrapping ) completely dull. I must ad that the sanding procedure must be completed on the whole car before attempting to start buffing.
All during this sanding process it is imparative that you keep the work surface, and your paper, soaking wet. Normally most people in the trade sand with one hand, and use the other hand to keep the sanding surface dripping wet, with either a large rag, a sponge, or directly with running water using a rubber hose held close to the surface.
In closing, ( and you will wonder why I didn't mention it before ) I would strongly recommend that you do not attempt to do this by yourself, it being your first try. I beautifully painted Corvette such as yours, is not really the right place to go through the learning process. I admire your courage, but if you have a mishap, and slightly cut through the surface, it's back to the paint shop once again, and I'm sure this is not something that will please you.
I can still remember the first time I did a complete job of sanding and polishing a Corvette. After having someone over for a few hours for some " hands on " It took me a complete week of evenings in the garage to sand and buff the complete car. So this is definately not a weekend thing.
Get help, have a professional come over and get you started so that you can see for yourself exactly what is involved. This response may seem lengthly but believe me, I have not even scratched the surface ( no pun intended ) as yet.
P.S. Regarding the paper, some sell the paper in smaller sizes then is normally seen , so you will need to adjust the size accordingly
Good luck with the work and the decisions
Bob