I store the generator with no fuel in it, and when I do the final shutdown once the power comes back, I run it dry so there's minimal residual fuel. I also drain the fuel lines. This was a lesson learned from the service guys who told me it's absolutely necessary due to ethanol damage, and no additive is better than no ethanol sotred in-system.
The manual for my generator says to either run it under load for 20 minutes every fourteen days, or to follow the long-term storage procedure. The long-term storage procedure has me changing the oil, draining the fuel line and the carburetor, squirting a little oil into the cylinder and turning it over a couple of times. So the gas tank will be full but the engine won't have any fuel in it.