Over a 23 year period we've had a PUP and 2 hybrid trailers. We store outside, next to our garage, on a gravel pad, have never covered them, never did anything special with the cushions. We do have have mice from a natural area behind our home, some even come into the garage, which is attached to our house and right next to the trailers. We've never had mice in the trailers or insects, and neither has my dad, who's '77 Jayco trailer is parked on the same pad for the past 20 some odd years. The trick is to make sure that any potential food source is removed from the trailer. And clean the inside really good when putting it to bed. Of course we also do so after every trip, but the point being is to remove all potential food sources, even trace.
Since you have indoor storage you might want to leave one of your push out windows open for a little extra ventilation.
If you have dogs or cats, avoid poisons. Dogs and cats both will eat mice, small critters, and insects. If they are eating critters that ate the poison, they can get sick or even die.
EDIT: I do cover my AC and tires.
2013 Jayco Jayfeather X20 E, 2008 GMC Sierra 1500 Crew Cab Z71 SLE