Agree with what extrap said about a private party being the best choice. With a private party, you have time to do a PPI, drive the car, review maintenance records, get a Carfax, etc. You get to assess the seller as well. Old Bedouin wisdom says, "when buying a camel, look one part to the camel, and two parts to the seller."
BaT is next best. Most GTs will be "Premium auctions" which will give you 10 days to look the car over and get a PPI before the auction ends. The auctions pictures usually include the maintenance records and a Carfax report, so you can see those too.
Dealers can be good or bad, depending. If the dealer is selling it on consignment from a private owner, and you can see the maintenance records and get a PPI, then that's almost as good as a private seller. Beware dealers who are flippers.
The TV auction houses are the absolute bottom, IMO. There, you have to be very knowledgable and make damn sure you know what you are getting. You will have very little time or hands-on to make your decision and probably no records.
GT experts: I also recommend Rob Henderson, "GT@50". He's in Seattle. Where are you? Where are you looking for a GT?