A garage or a cellar is the obvious place to put what will not fit indoors, and it is where household storage goes wrong most often. The room is cheap space, so it gets filled, and nobody looks properly at what is happening to the contents until something is ruined.
Check the room before you trust it with anything
Go down with a torch on a cold morning rather than a warm afternoon. You are looking for three things, and they have different answers.
Beads of water on the walls or on cold pipes, worst in winter, spread over a surface: that is condensation, and it responds to ventilation and to keeping the temperature steady.
A single patch with a defined edge, or a line about a foot up from the floor that reappears after it dries: that is water arriving from outside, and no amount of airing fixes it.
Actual puddling after heavy rain, however shallow, means the room floods. Nothing goes on that floor again.
If the boxes have already come out damp
This is the part people skip. Mustiness on cardboard, a tide line on a box, paper that has gone wavy: the contents are a salvage question, but the room is a building question, and the second one is the one that recurs. At that stage it wants someone who deals with flood restoration in Tucson or wherever you happen to be, because finding where the water comes in is a different trade from drying a room out, and both have to happen before anything goes back.
Get everything off the floor and off the walls
Shelving on the long wall, feet of plastic or metal rather than chipboard, and nothing touching the external wall behind it. A gap of fifty millimetres lets air move and stops a cold wall transferring straight into whatever is against it.
Pallets are not shelving. They raise a box by a hundred millimetres and they absorb water themselves, so they ruin the second thing they are asked to do.
Containers, labels and the things that should never go down there
Lidded plastic boxes, not cardboard. Cardboard wicks, sags and feeds mould. Clear boxes save you opening six to find one thing, and a label on the end that faces out saves you more.
Some things simply do not belong in an unheated outbuilding at all, whatever the container: photographs, documents you cannot replace, anything leather, anything with glue in its binding, and electronics you intend to use again. Those want a cupboard in the warm part of the house, even if it means giving up space you would rather keep.
The quarterly habit
Once a season, open two boxes at random from the back of the bottom shelf. The back and the bottom are where it starts. If both are dry and smell of nothing, the system is working. If either smells of cellar, something has changed in the room and you want to know now rather than in two years, when the box underneath has been quietly soaking.