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Just make sure it has good tires on it! I have some junk Sumitomo HTR Z II's and they are crap they washout and squeal like crazy around every corner, stock F-bodies are keeping up with me without a problem.
One benefit of the C5 Corvette is that it has an awesome amount of adjustability built into the chassis. Lots of camber adjustability up front, reasonable amount of camber adjustability in the rear. With the stock leaf springs, you can still do a lot of corner balancing and can adjust the rake. Even with the stock leaf springs and stock adjusters, my car is within five pounds in cross-weight.
Of course, it's just as easy to make the car evil handling as well.
So, as previous posts have said, learn the car, get some seat time, and then take advantage of all the "free" adjustability that GM designed into the vehicle.
Since the car is secondhand, the advice to check stuff is correct.
1) Alignment: Get it checked by a competent shop. You're looking for -1.1 to -2.0 camber in front, -1 to -1.5 in back. Slight toe out in front is OK, slight toe in rear is ok. Square is also OK, esp. for street track hybrid alignment.
2) Ride height. Slammed is a no-no for handling. The best bet is about -20mm down from stock. More is doable, but depends on your preferences. Too much more (-50mm or more) is going to adversely affect your handling.
3) Differential. If the diff has not been cared for, you'll hear it. Good idea to check the fluid level and scent. If it smells burnt, replace the fluid. Do some slow, non-wheelspin figure eights to get it relubed and it'll turn better.
4) Tires and tire pressure. Easy. Set to 30 around. Lower is bad for handling, pretty much. Get some non-runflat tires, and AAA for flats. Much improved handling there.