Pete, what's the real criteria?
While it's nice and all to get cheap body parts, I'd say P71 is more correct to find a clean car (having worked on a lightly rusted Alfa recently, I'd agree more, but the rust in my eyes makes it tough to type).
Cheap AND pleasurable? While VW's can be cool, how much do you have to put in them to be really fun to drive? Is it ok that you have to modify the car to be pleasurable? Like a Fiat 850 can be a blast, it's probably a lot easier to do a 124 Spider.
It's such a broad question. And how old is old? Does the 80's mustang even qualify? Or will it have to be some 70's car where the emissions controls are easily modified?
How cheap is cheap? Cheap on time, cheap on the wallet? Some cars DO satisfy both, but it's pretty rare.
I'd still lay out a '91 Miata. Simple 1600, spritely, slow enough for insurance to be cheap, large support group, pretty easy to find cheap. And if you were crazy enough, I'm sure you could do a carb conversion....
Or even a late 80's/early 90's Civic. Well sorted from the early models, LOTS of performance parts, and still fast enough to tear up the STS class. On top of that, can find world class fuel economy out of many (picture a SI engine in a HF, with the HF gearbox- autocross friendly gearing + long highway miles).
And I know there are a lot of people who love tearing up Festivas. Not sure why, but they sure do love them.
Eric