On and old mower one thing to check carefully is the deck especially the one with the cheap thin metal.
A new deck can cost serious money and may not even be available'
Engine problems can be fixed for a coupe; hundred or less but a new deck will be serious $$$$$$$$
Since you can not inspect a deck on e bay I would never buy from their.
I want to see what I'm buying but I never have bought a used mower I prefer to buy new then sell in 20 years and let someone else worry about keeping it running.