Professional help
Most members, myself included, will do their best to come up with various lists of areas, item's, parts, etc. that you should be looking into. Sadly even if you are on the lookout for the troubled areas, it often takes a trained eye, to properly catch the problems.
My recommendations would be to try and get in touch with someone who can offer you, for a fee, professional assistance in properly evaluating the present condition of the vehicle. What ever fees are charged, will on represent a fraction of the cost's of repairing a flawed vehicle. It's really a small price to pay to insure that your prospective purchase, will be something that will turn out to be a good investment, and not a long term money pit.
Lastly, and I know this is going to ruffle more then a few feathers, the 64 model, is not the most sought after model year. I don't mean any dis-respect towards anyone, or their vehicles, but thirty some years of buying, and selling have proved to me many times, that it's actually the less desirable of all the mid-years.
I have no logical explanation as to why, but it has just proved to be the case during all the years I have been working with the 63-67 model years Corvettes.
Good luck with your decisions
Stepinwolf