Chances are that when you get the mechanic's report and Carfax report, you'll know which candidate Corvette you want. Now comes the stressful period where you negotiate the purchase price. Sometimes it's easy - the seller says "This is the price. Take it or leave it." But more often, there's an asking price and you have to decide what to offer.
Some people believe the old adage that the first person to name a price "loses" the negotiation. So they dance around with "what's your lowest price?" or "Make me an offer." I think those habits are silly, because everyone knows their bottom line price already. You might pay a little more than the seller's rock-bottom price, or the seller might take a little less than he or she was hoping to get, but it's really all about whether you get the car for a price that seems worthy and fair to you. In five years, will it really matter if you paid $20,500 or $21,000 for your beloved 'Vette?
One rule to remember: if you're buying a lower-priced car, paying in cash always works to the buyer's advantage.
More often than not, it's possible to negotiate a price that works for both buyer and seller, and you can conclude the transaction amicably. If possible, get the seller to meet you at the DMV office so you can conclude the title and registration transfer paperwork on the spot. Then you get to drive home in your new Corvette.