Full tank is better than part full due to condensation from temp swings.
I always fog out engines before storing them. Meaning add 10-12 ounces per gallon of either Marvel Mystery oil, or automatic transmission fluid, Rig up a fuel line to any container, and run the bike on this mixture. You will have to apply a fair amount of throttle to keep from fouling out. You only need to do this for 15-20 seconds. While it is revving/smoking like a forest fire, disconnect the fuel, and let the carb run dry.
After that cap off the exhaust, and intake with plastic bags, and do an oil change for the engine. Fresh oil will protect the internals.
Pull out the battery, and store it away from freezing temps.
I prefer Sta-Bil to all the other snake oils. Use the BLUE Sta-Bil made for ethanol fuel cause like B&L said, eth. will attract water.
In the spring pull off the bags, and install a new spark plug, and kick it over. It will smoke for 20 or so seconds but it will clear. It will run sh**ty because of the old gas so I would also suggest siphoning it out, and starting w/ fresh fuel.
This only takes 1/2 hour from start to finish but you can technically store the bike for decades this way.