Few things you need to consider:

i) Check for leakages specially from and around the engine area. How can you check? Drive the car a couple of miles and then stop and check the underneath after 15 - 20 minutes. Leakage will be immediately identifiable.

ii) Keep an ear out of strane noises. They are usually made by either worn out parts or some damaged parts inside the transmission or braking systems. Remember that abnormal sounds shouldn't come even if it is an old car.

iii) Check how much smoke it emits specially during starting and changing into low gears. If there is a lot of smoke the engine may need repair and maintenance before you can take it out on the road.

iv) Shocks of old cars are usually bad so my suggestion would be to check them if they are overly bad and give a lot of bumps otherwise if they are somewhat in bad shape, you can live with them.

v) Last but not the least, check the internal guages and buttons. Indicators, AC, vipers etc.

vi) Try to drive the car three or four days before you agree to pay for it.