Usually with every used machine that I purchase, I always go through it and do a tune-up. If it were mine, I'd most likely buy a JD tune up/maintenance kit that includes oil, oil filter, spark plug, air filter and fuel filter. This way it'll all be ready for the mowing season.
Maybe clean it all up nice and good too if it's not already, totally your preference. Checking the condition of the belts and having the blades sharpened (if they need it) might not be a bad idea either.
Ditto what Austen said. Also if it is an auto (hydro) transmission instead of a gear shift transmission I would make sure to clean all the debris off the transmission cooling fins and check to make sure the cooling fan is in good shape and not missing any blades. One more thing would be to check the fuel line to make sure it has not started to crack and perhaps needs replaced.