I've been asked that question at least a hundred times. I am in no way consider myself a pro but these are things I look for when buying a car in general.
The most important thing to look for is RUST!
Once rust gets into these cars they screw up everything! You have to look thoroughly to make sure there is nothing hidden. Check the trunk, around the taillights, take off the plastic trim around the trunk lock, see if there is any rust brewing up where you cant see them.
Check the door sills, driver and passenger floor, jacking points etc.. Most E30s with a sunroof begin to leak water inside and rust might start popping up in those places. It may also cause the roof to start rusting.
Also double check the wheel arches, strut mounting points. Even if they don't seem to have rust, they might be covered up by some cheap body shop and they will pop up later on.
After the rust inspection is passed, check the engine bay:
Does the engine look like its leaking? oil seeping anywhere? does anything look out of place. These cars are really reliable and can run forever if they are taken care of. Turn it on, check for engine noises. Look for the color name on the right top corner of the engine bay, the chassis number on the firewall, and the plaque with info on the radiator support.
Done with engine bay, check the interior:
Cracked dash is a common issue, nothing to worry about you can always replace it if everything is going well so far. Check if the heat is working, blowing correctly. Turn on the lights inside, check if the cluster is working, lights in the dash, make sure there are no electrical issues. Its a 30 year old car, wear is going to be evident, but to a certain degree. You can tell if its been abused or not.
Now take it for a spin:
Make sure to check any noises from the differential, and if there is any clunk noises when you shift gears. Steering is pretty tight for a car its age, it does not feel like an old car when you drive it, so you can feel if there is anything wrong with the suspension or steering etc..
Now you can talk price :)