I store mine in my unconditioned basement, and they do well.

If you're gonna store them in a shed, I'd recommend you try to do the following:

Pick a raised area of land to build the shed on. If none are available, get a small load of crushed rock or free draining soil in to build a pad to put the shed on, about 5-6" high. This will eliminate the possibility of standing water inside or under the shed.

Build a pressure treated base for the shed. This lets you raise your floor so it's not in contact with the ground.

Install a floor in the shed. If you don't want to buy the floor kit, just use some exterior grade plywood and your ingenuity to make one. A sheet of vapour barrier under the shed floor (even staple gunned to the bottom of the plywood flooring) will prevent ground moisture from entering your shed.

Anchor the shed to the pressure treated base. If you're in an exposed high wind area, consider driving some anchors in to keep things put.

When you build the shed, caulk any seams that aren't sealed. Be sure the shed has some ventilation at roof level. This could be soffet vents (vents under the roof edges, like many houses) or gable vents. At least 2 would be best to ensure ventilation, as always one needs an inlet and an outlet.

Be sure there are no gaps larger than 1/2" in the walls, floors or doors. Mice will get in them. Mice like shelter. Mice eat anything. Seal gaps with whatever is necessary. If you use spray foam or something similar, put stainless steel wool (pot scrubbers) in first, then foam. Mice won't chew thru that stuff.

Try to keep the planes off the floor. Think wall and ceiling racks, if possible.

A light colored shed and roof will vary in temperature less than a dark one.

Basically, you need to prevent water and pest entry. Water comes from the ground or the sky, and pests come from anywhere. Ventilation and color choice will help stabilize the climate inside a bit, and let any moisture that does get in to get out.

Make sure you check out local building code and permit requirements, as this sort of thing is one place where begging forgiveness may not be easier than asking permission, if you know what I mean.

One last thing. Consider installing at least one light in the shed, as you may find yourself returning home after dark, when flying to dusk, and it's hard not to hangar rash planes in the dark!

Good luck,

J