Dickymint, thats one niiiiiccee 156
to the OP - drive it, listen for squeaks going over bumps (find some speedbumps or something like that). Squeaks from behind the dash are usually upper arm bushes - 'bout £100 for new arms and then fit yourself or pay the labour. Squeaks or "rattles" / vibrations from down near your feet tend to be ARB bushes, drop links or lower arm balljoints. If its the balljoints you normally get vague steering and some wobble on hard driving. That can also be track rod ends though, but you can check those out at full lock if you get your hand behind the wheel.
Check all the electrics work (ALL of em). make sure the airbag warning light is genuinely off and not taped over. Some people remove the bulb - no checking that without diagnostics or panel removal! water temp should be a steady 90 when warm, although some 156 gauges can be rather off. if it seems to warm when stood and cool quite a bit when driving it could need a thermostat. Not too expensive or difficult tbh.
Other than that, check the history out (as already mentioned the cambelt is critical - balancer belt and tensioner too on the 2.0 so it's a slightly pricier change) and see if it "feels right" on the test drive. Check inboard of the sill as well, underneath, for rust.
they're most of the basics I think. I'm sure there's more but you have to accept SOME compromises at the price you're looking at too I guess?
btw cambelt (as already mentioned in this thread) is a job for someone who knows TS engines. The diesel one is a fair bit easier. I would also vote for a good 2.4 but they're very heavy on suspension parts (as I know all too well!