If the engine has had a "major overhaul" and hence zero timed (meeting or exceeding all manufacturers specs and tolerances and mandatory parts replaced), then it should be issued with a new logbook starting at zero hours. This is the only overhaul I'd be concerned with, if it had an "overhaul" but not zero timed then the engine should be considered to have run the same number of hours as before the overhaul for the purpose of financial negotiations if you get what I mean !?!
There is also TBO which is the Time Between (major) Overhaul recommended by the manufacturer. An engine near to TBO should be considered not worth much above its core value, even if the aeroplane is running fine. You can go beyond TBO for private ops and run the engine "on condition" if you want, though personally I'd get a major overhaul done by TBO. Engine overhauls cost anywhere from £15000 to £30000 for typical 150-250HP types. Our TO360 cost £28,000 to overhaul (zero time), though we had it balanced at the same time. So when factoring cost of the aeroplane you should take this rebuild figure into account and an aeroplane with low hours on the engine could be worth say £25000 more than one at TBO.