I see a couple issues. Truck renting is expensive as well as renting a storage place. For the cost of renting a truck you could just as easily buy a beat up old trailer.
Also consider if somehting happens that makes you relocate and need to get to those supplies chances are the owners of the storage place have locked up and went home as well as the owners of the truck renatl place. To me renting a truck and/or storage rely too much on someone else.
I'm watching craigslist now for a small beat up trailer. if you build a trailer yourself and want to license it then you hve to jumo through a lot of hoops to get it safety inspected, but if you buy a beater and license it then replace every part except the serial number your still legal. I want something small, just a single axel with a bed and bathroom and little else, small enough to roll into the garage.