Regardless of what you do, what you don't want to do is leave a gas tank partially full. Gasahol can only pick up moisture if there is air present. Fill the tank all of the way and there is very little room for air. You should use a fuel stabilizer of the tank is full.
You should also put a tablespoon of oil in the spark plug hole and then turn the engine over a few turns. This will get a good coating of oil on the cylinder walls and piston rings prior to storage. It will smoke a bit when you restart the engine in the spring.
With 2 stroke and hybrid 2/4 stroke engines, you should put the oil down the throat of the carb instead.