Genny oil

All oils will do an excellent job. "In theory" the synthetics says you get longer oil change periods as the only real advantage. I am going to change the oil on the same schedule whether it comes from a dinosaur or the laboratory. YMMV!

I would run Synth in any newer engine, especially one like in a generator that will be running for long periods under load. I like to feel safe if I have to run longer between changes, with no worries about the oil failing.

I just want to do what is best for it,I don't want any trouble !!!!

No. Unless you have money you like to throw away.

It will not hurt
, but not necessary.