A significant number of the affordable classics you can find for sale have ugly exteriors with running mechanicals, but paint/interior can be extremely expensive. What about the nice looking cars that have a busted motor, can those be a good deal? The answer is yes, but only if the engines are cheap to rebuild - so stay away from 6.9 liter M100 Mercedes V8s and stick with something simple like a Volvo inline-4. Here is a 1971 Volvo 1800E that needs engine work, offered for $5,000 or best offer here on craigslist, located in Orange County, CA.
This '71 1800E has had a nose job (see a stock face here) from a previous owner who didn't like all the chrome, according to the current seller. It makes the front end look even more like a fish mouth and the quality of this sort of customization is tantamount of determining if you want the car. Cheap/sloppy bondo work needs to be avoided because returning to stock will be pricey, but a finely done nose job could be left alone. Even with the T-bird style hood scoop, this car would be a steal at $5k...if it ran...
Under the hood we get to the root of the low asking price, the little pushrod 2.0 liter B20 engine has some bottom end issues. Being a later 1800E, this car should be fitted with Bosch D-Jetronic fuel injection, (in which fueling is proportional to manifold pressure, D for the German Druck, meaning pressure) but it has been backdated to a single carb setup. Expect something in the range of 125 horsepower, when things run. Tear it apart and take a look -- a new block for a B20 shouldn't be hard to find (or expensive) since Volvo used these things in everything from their sporty 2-seaters to 4X4 military vehicles. If you are going to modify it, stay away from Chevy 350 V8 swaps and do something like a boosted Volvo inline-5.
The interior is filthy, but liveable. Many of the parts you see inside this car are available from aftermarket suppliers -- carpet kits, seats and such can be found without too much searching.
See another sub $5k 1800 that isn't a total rust bucket? firstname.lastname@example.org