Morning Dave
Welcome to the Forum
As with any Used car purchase History History History don't just check the service history also check it's MOT History and recall history. MOT history is useful as you can see if advisories have been attended to, recurring advisories to me indicate poor care and maintenance.
Tyres are they all in good condition, no odd wear patterns which would indicate worn suspension. While looking at the tyres check the wheels look for Kerbing scrapes or cracks and general condition. Body work should be in good condition with no big dents or scratches and no peeling lacquer
Inside seats and carpets not ripped or torn and in good condition. Do all the bells and whistles work try everything at least twice while you're in there.
Check under the car for signs of leaks on the floor, check oil and coolant levels, the engine should be cold if it has already been run question why? does it have a cold start issue perhaps? Run the engine and let it warm up again check for leaks, rattles, knocks or other noises. If your happy then the test drive the car should be quiet on the road with smooth gear changes (manual or Auto) Finally make sure AC/Heater and all controls work for the final time. If your happy and no issues OK However unless your competent with the spanners if there are any issues look elsewhere there are no simple fixes so if the seller is trying " you can get those on Ebay for a tenner easy fix " or the " never use it so it didn't bother me " Just ask yourself why if it's easy didn't they do it?
If you're buying from a Garage you will have some protection under the Sale of Goods act, if a Private sale take extra care as you will not have that protection.
Hope all goes well with the viewing
Dave