If you can rebuild a Lycoming and it flies, literally , then a mower engine will not cause you any grief, other than by worrying about the massive clearances and lack thrust protection & bearings .
If it is a B & S then it will be dirt cheap as B &S parts are too cheap ( When you can get them )
Kohler parts are closer to proper price so Kohlers are a bit more expensive
Kawasaki parts are dearer still and can run to double what the equivalent B & S parts costs ..
Loncin parts ( Toro branded engnes ) can be a problem as Toro & MTD are playing things close to the chest forcing most to but branded parts from the dealers .
Usually the break down is parts 1/3 labour 2/3 so if your labour is involved it makes rebuilds very reasonable .
However no decisions can be made till a proper inspection of the engine is done .
The other problem is of course time and how close to the end of the mowing season you are.
Very soon surplus retailers like
SURPLUS CENTER
Small Engine Warehouse
small engine suppliers
Will start getting in this seasons leftover engines so prices will be quite low for a while