Is Public Storage a safe place to store stuff?

I can't move into my new apartment until Oct 15, but school has already started for 2 weeks by this time, so I don't wanna waste too much time on moving stuff. You know quizzes and exams are beginning in that week. Therefore, I decide to place furnitures into a Public Storage which is near my new home. Is it a good idea? And I wanna know how to buy insurance for my stuff. thx!