If it didn't have an oil change, you might want to do that.
IF the oil doesn't look "too bad", you might want to mow first, and then drain it when warm.

Air cleaner and new spark plug might not be a bad idea, but may not be necessary. Plugs usually last several years or more, depending on how much the engine is used.

Air cleaner can be very dependent on conditions you mow in. Dusty, replace more frequently than if you mow on lush, deep, moist grass.
Depending on the mower, AC's vary greatly in price.

See the post about storing for 6 months below.

BTW, I like to do my oil change when storing it for the winter. That way, you don't have the "toxins", for lack of a better word, sitting in the crankcase over winter.