How To Move Storage Units.. Truck And Van Rentals U-Haul And Penske Box truck rentals is definitely the most common way that most of you will be transporting your goods from the storage unit to your location. There’s a few options that I typically use it may be different in your area depending on what you have available to you. Keep in mind this somewhat can get expensive and you will be up against the clock so try to use family or friends vehicles rough it out at the beginning to save a little