For most of the OPEs I have, that run for maybe a couple of hours at a time, I use whatever is laying around or whatever I've picked up dirt cheap, as long as it's at least a thirty.
For something like a generator, though, especially a diesel one, that might be called to run for many hours at a time, I'd be a little more picky.
For the little gas genny we have, I use T5 10W-30.
T6 5W-40 would also be a good choice.
OTOH, Delcac 1300 15W-40, of which I have a few gallons, would also likely work well.
What I'm saying is that it depends upon how the engine will be used.
I'd use a premium oil in a generator that might be called upon to run for many hours.
If it were a diesel, I'd be sure to use a suitable oil.