I give mine a good 10 count if it's been sitting for a while, then crank for a few seconds. If no start, I give the prime another 5 count, and it almost always fires right up then.
As for winter storage, I'll echo the others and say once a month under some load. But I'll add that you should store it with stabilized fuel. The ethanol fuel that we get these days is no good after sitting for some time. The carb in the generator can get gummed up easily too (my FIL has replaced his carb twice for this, you'd think he would learn). I find that when I stabilize the fuel, things run A LOT smoother after a "long sleep" in storage.
I use Schaeffer's fuel stabilizer that I get from one of my clients who owns a diesel shop. He swears by it, and it has done well for me.
-2018 Greyhawk 29MV
-1994 Jeep Wrangler YJ (Toad)
-2015 Jeep Grand Cherokee Limited (Soon to be Toad)
-2014 Jay Flight 28BHBE & Ram 2500 6.4L CC 4x4 (sold)