Go with your dream, get the vette, 69-81 models can be found in decent shape for as low as $4-6k, expect to drop any old crate GM motor in it, $3k, and paint it, ~$1500, seats, interior parts etc are all readily available aftermarket. The stock engines were very restricted, remember there was an oil crisis, but props to chevy for building a real V8, not a Mustang II !! If you pull all the polution crap off, its pretty ez to get solid horsepower out of the engine as is, replace the heads and carb, followed by sidepipes, all fairly ez to accomplish even for a beginner, and you'll have a screamer.
You will be constantly working on the car, but there are lots of clubs and books to help you.
The car will be amazing in a straight line, not so good to race on a track with, its very easy to slide out of control with all that power to the rear wheels in such a light car.
A 63-67 is a much nicer car, the 'midyears' but good luck finding a project car for under 20K. 63-64's are cheaper since they usually have drum brakes, a kit is available for $1200 to convert the front to discs. The club guys will give you the evil eye, but I'm in the process of installing the kit now, I'm much more concerned about having a dual master cylinder than having a stock 63.