you want to have them lay flat or in stacks of 5 boards max and put them somewhere with stable conditions in terms of temperature and humidity. no extremes. i would keep them aways from any warm spotlights. dry heat will make the board more brittle. high humidity can go through small cracks sog the board. when the water evaporates fast, warping occures.
in the shops i worked at the boards that warped fastest were those next to the windows or the ones that got heatblasted periodically by the ceiling lights. say you hang em up like many shops do they will warp where they are not fixated, so say you hang em up on some screws or nails at the front truck holes, the bottom part will warp even more.
shrink/seran wrapping won't do alot if the boards are brand new and still coated with a finisher. i would take em out of the shrink wrap to be honest since i wouldn't want any moisture to get trapped in there if i store em for longer.
i don't keep a lot of spare boards nowadays but i had good results with storing them under my bed.
basically keep them at a comfortable room climate and avoid them being exposed to changes of temperature and humidity.
the worst thing you could do to your boards is leave them in the trunk of your car in the winter, especially when you have a mid or rear engine. it will go from super cold to very warm and back all the time and this is what warps boards. generally cartrunks are the worst long term storage for decks unless that car doesn't get moved and the trunk is dry.
i can't back any of this up scientifically, this is all from observation and working in shops and distro warehouses throughout two decades of me skating.
EDIT: removed my second post to add it into this one
you better store them on the side / edge rather than on top of each other
i know i said the opposite(stacking 5 boards max) but i could see this working better if you have different shapes. if it's the same shape i'd still stack em but put some sort of buffer material between them.