I have metal bins my husband bought from Lowes and installed them in the closet of my sewing room. I separate my fabrics by color. And I have a separate bin for childrens fabrics. You can also stack fabrics on top of the bins so I have my solids separate and my white on white backgrounds fabrics separate.
This works great for me because you can see through the metal bin, the fabric can breath and it is away from sunlight.
I would never put fabric in drawers, you would have to rummage through to much to find a fabric, and I don't think the fabric can breath. If you put fabric on shelves make sure they are in a closet away from light. You want easy accessability and allow the fabric to breath and keep it away from sunlight.
Never store fabric in plastic bins. The fabric cannot breath and formaldahyde from the fabrics (especially unwashed fabric)
will accumulate in the plastic bins.