PG, you would check the basic mechanics by simple non-intrusive tests. With engines you are paying for that usually means firing them up then listening and watching. Free (mostly nature strip) engines probably won't start so you end up taking a punt on them being fixable. You will seldom find a horizontal crankshaft engine on a nature strip though, so that option involves a mix-and-match of parts. Hence, finding a running $50 horizontal-crankshaft engine that just needs minor repairs, is probably easier. You have to know as much as Bruce or Joe about the detailed interchangeability of parts to make the nature-strip option work - but you might be able to ask them specific questions here, to get the answers you need.
As far as I know all of the 9-series engines had seven-eighths inch shafts, but Bruce or Joe could tell you with certainty.
You can just start off with a plan to do this job without paying for machining. I doubt it would be a good idea to bore your clutch hub to fit a 9 cubic inch engine, so you need a five-eighths crankshaft. The simplest answer is to find someone (probably through this site) who has a spare Briggs, Honda or Tecumseh horizontal-crankshaft engine with that size shaft. They should all be interchangeable as far as engine mounting is concerned (Bruce could verify that). Then all you have to do is adapt the bottom end of your existing speed control cable to fit the new governor.
You may find that the most-available engine has less power than you are used to - the 60102 is only 2 hp instead of 2.5. I doubt this would be of any practical importance on a cylinder mower of 17" cut or less.