The most common storage booking is one-way: out of the family home, into a self-storage unit. The driver loads at the home, transports to the storage facility, and unloads into your unit. Most self-storage sites have trolleys, lifts and dollies on site. The driver uses them as part of the unloading time you have booked.
Van size should match the unit. A 10-25 sq ft unit fits in a medium van. For anything larger, a Luton is usually the right call. Most units are accessed via lift or ground floor, but some facilities have outdoor or upper-floor units that take longer to load. Flag it in the booking notes and the driver allocates the right time.