The very best way to store them is in loaded shells ready to shoot. Lacking that, any dry area will do as long as it is not real hot. Attics, small metal storage buildings and basements are usually not the best. A garage, work room or under your bed would be OK.
I have things in the basement. I have a dehumidifier(sp) and I have put powder in one can and primers in amother for good reasons. The cans that I use are the military ammo cans. I will buy them and the first thing I do is open them and see if there is any pressure in them. Air coming out of them. That means that they are air tight. If they have rust in them I will not buy them. There will be a leak in them some place. An Army surpluse store will have them but I have found gun shows to have the best price and selection.
Store powder it OEM containers; don't transfer it to a stronger (ie. "fireproof" container and do not store it in a strong locker or closet. OEM containers are designed to allow the powder to burn in a fire rather than build pressure and explode. I just keep mine on shelves in a dry basement.
Primers are stored on a floor-level shelf on the other side of the room.