A lot of folks will have
their favorite tires and will recommend them. But what you may want to add to your question is what type of driving you will be doing. Street use only? Occasional autocross events, maybe a track day once a year?? What sort of weather will you be driving in, dry pavement, wet roads, ice or snow?
There are a wide variety of tires by brand name and level of performance in dry and/or wet conditions and of course cost will also play a big part in a selection.
For my personal suggestion, I have a set of Bridgestone Potenza's (RE730) on my 92 vert that has seen both dry and wet pavement, a couple of seasons of local autocross events and 3 track days at Portland (OR) Int'l Raceway where the track temps reached 130+ degrees. With about 30K miles on them, they have about 75% tread left. They are very quiet on the road and are much stickier than the original Goodyear GS-C's ever thought of being.
Check out the Tire Rack
www.tirerack.com for some good prices. If there is a Discount Tire in your area, they will make every attempt to match tire price quotes fro other sources. The Tire Rack website also has some customer tire reviews that you can read to possibly help in your decision.
To search for tires, start here:
http://www.tirerack.com/tires/index.jsp On the right side, select "Browse by Tire Brand" That will open a page that lists the manufacturers where you can choose a tire by type. Just clikc on the brand name. You should look at those tires listed as "Max Performance-Summer" or "Ultra High Performance Summer". These type of tires are suitable for the performance levels that your Vette is capable of and will be at the very minimum, be equal to the OEM GS-C tire.
The individual tire page that opens will have a graph that indicates the tires ability to perform in various road conditions based on the reviews. The higher the number, the better the tire should perform.