Also make sure the bike doesn't have a lot of rust, fixed gear bikes crack easier.
Also flick the frame with your finger, if it makes a small ping, it is good quality steel. If it makes a dull thud, it is bad steel and you should not consider buying.
Up next once I build more on the Schwinn.
Gear ratios
pedals
brakes
bottom brackets
seatposts
chains
and more