The first thing i look at are the body lines....the gaps between any part of the body that can be taken off, especially where the fenders meet up with the windshield and cowl panel area. If the car has ever been wrecked, it's really hard to get these to line up ever again, unless they really do it right (in which case you probably won't have to worry about it). Then get under the hood and look at the radiator core supports, top and bottom for damage, and look around the frame rails while you're under there.
Then i get under the back and and look at the rear end, specifically where the upper and
lower control arms attach to the floor pan. These are commonly called "torque boxes" and are a high stress point on a car that gets a lot of beating, and they'll actually rip out over time. If there's ANY rust in this area, i usually steer away from the car altogether unless it's really minor.
Then i move up the bottm and just look for rusty floor pans or frame rails, look up around the fender wells for rust etc. Open the trunk and pull up the carpet and look there. (if you haven't guessed, i F'in HATE rust). I'd rather swap an engine than deal with rust.
If all that is A-O-K, then i'd turn my attention to the engine and transmission.
Rev the engine until it hits the rev limiter....if the owner/seller doesn't like that or won't let you, don't buy the car! Some cars will run awesome on just a start up and idle but once you start driving them and put them under load they show their ugly side. An average running 302 should be able to take a rev limiter hit with no problem at all, and when you do hit it, look out back for smoke. The color of the smoke is going to tell you if it's burning oil or coolant etc.
Look for engine leaks of all kinds (but honestly with a 2k budget, you should expect some).
Sit down next to the front wheels (put a leg on either side of the tire) and grab a hold of the wheel with both ands and shake the hell out of it. If it moves a lot, it probably needs tie rods or worse. Also while it's running turn the wheel both ways and listen for the power steering pump to skreech and feel for play in the steering wheel.
If the seller doesn't mind, give it a good 1st/2nd gear burnout and see if it leaves both tire marks...if only one side marks then you probably need to rebuild the traction lock in the rear end.
Geez i've typed too much....someone else jump in