I have *always* stored my fabric folded on shelves inside an armoire with the doors closed.
Each shelf holds one or more stacks of fabric by color (depends on the size of the shelves) and I just lift out the whole stack of 60-90 fabrics (about 12-16" high) when I need to audition a color.
They are protected from light, fading, dust, dirt, mold, and 'loss' (really misplacement!) by this method.
My collection probably has over 800-900 different prints/designs of fabrics even though some are less than 1/3 yard. As fabrics cost so much and I have an extensive and even older collection, I look at them as the largest investment that I have made in my art. Therefore it is worth the cost of proper storage to me. Check out second hand stores for good armoires.
Jan in VA