We've been researching this a bit while trying to figure out the budget for a potential build. For us budget minded street oriented folks that won't be on the track and don't need every last bit of performance we've found the following.
For the standard wheels it looks like Nitto Invos are the most affordable option now that General Exlaim UHPs have been discontinued. General is apparently coming up with a replacement later in the year. The Nitto NT05 (?) seems a little cheaper, but I don't think they make them in a size that fits. Its a big jump up in price after that. The folks on the Corvette forums seemed to like the Nittos and the Generals as alternatives to the Goodyears that came on the Z06.
For the upgraded wheels, the BF Goodrich seem to be the most affordable, but I have no clue what the reputation is on that tire. But if you're upgrading wheels, then cost of the tires probably isn't as big a consideration for you.
I know nothing about the racier end of the tire spectrum, so the 10/10ths guys building track rockets can maybe speak to what works and what doesn't in that context.