Inspection for internal corrosion on the engine at the very least, probably with a boroscope. Don't run the engine, don't even turn it over by hand unless an engine mechanic has given you the OK to do so. If there is rust on the cylinder walls you'll only cause more scratching. Not good. You're probably also going to want to do a compression test once the engine runs. Obviously, expect a flat battery. Also expect to do an oil + oil filter change and spark plug change. If you do change the oil, get a metallic analysis done on the oil filter: the metal particles suspended in the oil can tell you a lot about engine health. Also check prop balance, particularly if it's a wooden prop.
Look for any places where water might have accumulated & frozen. Take a flashlight and a mirror on a stick. Check for wind damage to the aerodynamic controls if you're not 100% sure it was tied down correctly with gust locks and everything.
Put the aircraft on a level surface with a neutral background, take 10 steps back and take a good look. The human eye is surprisingly good at detecting asymmetry in things like angle of incidence. If possible bring an inclinometer (a very accurate digital spiritlevel) and check whether the angles left&right are equal (incidence, dihedral, up&down of flaps, up&down of ailerons, elevator).
Also check the paperwork is complete from day 0 if possible. Talk to the maintenance outfit, if any, preferably without the current owner present. Try to find out if any SB/AD are applicable and carried out. Check the W&B sheet.
From pictures I found on the internet this looks like a rag&tube plane. If that's correct, check the kind of dope that was used to impregnate the skin, and it's anti-UV properties. Check the tubes for corrosion.