I have that same Generac engine in a 6 year old, 13 kw, natual gas fueled, auto start version. So I will tell you what I know.
All the Generac techs (and the book) recommend Mobil 1 5W30. In my experience, it is a good all purpose oil. There is a Generac forum. In it, some owners complained that Mobil 1 5W30 tends to be "consumed", or burns off during an extended power outage (longer than 40 hours of continuous operation). When that happens, the low oil level causes the generator to automatically shut off to prevent engine damage.
We have had 48 hour power outages in both 90F and 5F temperatures. Since I am not a fan of refilling a generator's oil level in a blizzard, I decided to switch to an oil that
is a bit more "stout" than a thin, car oil. In the winter, I use Castrol 0W30. In the summer, I have been using Amsoil MCT 10W30 motorcycle oil. During summer temperatures, I have also used straight 30 weight. It is cheap and works well. So far, no problems here. These synthetic oils might sound like overkill, but I know one thing; If I am out of town, and the power is out for several days, my wife will not fool around with a generator, to see why it shut itself off. She will go to a hotel instead.