I store mine in my closet, a standard smallish bedroom closet built in the mid 70's, on a white metal shelving unit w/5 shelves. Smaller cuts, like FQ and jelly rolls, etc. are in clear shoe box size plastic bins. I store backing fabs on the built in shelf above the shelving unit.
The fabric is kept out of the light, is easy to see when I open the closet door and it can breathe easily.
Larger items, like fleeces, home dec, and other things less often used are out in my "annex", the attached garage in larger clear plastic bins. Ditto with my batting.