As I understand it, and being no expert, most gennys come without oil, and require the owner to install such before startup. I strongly suggest using the start-up oil recommended by the mfr at initial start-up, because if there are any manufacturing defects, and the genny has to be returned, using a non-recommended oil might very well be to your disadvantage. As voiding the warranty.
After successful initial run-in, choice of oil is up to you. Having a tachometer/engine hour meter will be of assistance in changing the oil.
Let's do a comparison. Water-cooled car engine running at 50 mph and given a (conservative) 4000 mile oil change interval. That is 80 hours non-stop running, which is considered by the car mfr as standard duty usage, and that's what they base their car oil change intervals on. Your genny probably has its' oil running a LOT hotter than your car engine which at least has the oil being air-cooled by the air running over the oil pan, and maybe an auxiliary oil cooler in your car. Your genny is probably sitting in a sheltered location, out of the wind-driven rain, and so running hotter than your car engine.
Again, being no expert, I'd suggest a fairly short oil change interval, and also suggest using the proper grade oil for your genny. Some folks have been known to rig up a floor fan to blow cooling air over their genny, and that is certainly something to consider. Most Gennys have no oil filter, so changing initial start-up oil at half the interval suggested by the mfr might not be a bad .
Engine oil is ruined by contaminants, and heat. We know this. With respect to most Gennys, since they have no oil filter, and no air flowing over them to cool the oil, and unfiltered contaminants are unrestrained, and run throughout the engine. Heat is something that stationary gennys placed out of the rain, and hence out of free-flowing air often face.
I'd suggest using grade of oil suggested by Mfr, and changing it often, maybe every 40 hours or so. It's usually less than a quart, and that oil gets mighty hot.
I have yet to see a single engine of any type ruined, or even damaged, by changing the oil too often. I certainly have seen some engines ruined by failure to change oil in a timely manner.
Good luck to you!