Many quilters organize their fabric according to color or fabric type such as batik, novelty, hand dyed, etc. How you divide your types of fabric would depend on what kinds and how much of each kind of fabric you have in your stash.
Fabric can be folded many ways. The most convenient would be to fold one yard size pieces and larger in half lengthwise matching the selvages. Then it can be wound around a long acrylic ruler similar to the way it is wound on the cardboard bolt. The acrylic ruler is slipped out and the fabric is folded in half with the selvage meeting the fold. This way when you are ready to use fabric you only unfold one fold and then unroll what you need. The remainder stays rolled ready to be refolded in half and placed back on the shelf. Shelves that are twelve inches wide are recommended for this type of fabric fold.
When placing fabric on open shelves they should be covered in some way to minimize light damage. Some quilters have hung a fabric curtain over their open shelves to protect their fabric from light damage. A pull down window shade covered with flannel that doubles for a design wall would work well also.
Fabric can be folded and placed in plastic totes. How you fold your fabric would depend on the size of plastic tote that you are using. It is important to be consistent in how you fold your fabric so I will always fit back into the totes when you are finished. Sweater box size totes are an excellent choice as they are not too heavy when full. A larger tote could become very heavy when full of fabric. If possible purchase all of your totes the same size and the same style. That way they will stack easily in any configuration you would want your fabric. Some have said you need to drill holes in your plastic totes so the fabric can have air to "breathe". Some of my totes are so full the lid is not on tightly, leaving an opening for air exchange. I have had my fabric in totes for many years and have not had any damage to my fabric.
Half-yard pieces and fat quarters may be folded and placed in small totes, baskets, or drawers. Anything smaller could be placed in totes or baskets according to color or fabric type.
Another fabric storage idea that I use. I prewash the fabric first. Then fold it as I would for cutting with the salvages meeting and then over again with the fold meeting the salages. Then accordian fold it as I would if I were to cut it. That way I know when I take it out to use it, it is ready for cutting and I know it has been preshrunk and all set for the new quilt I will be making.
The system you choose may depend on how much fabric you have in your "stash", the size of your storage space and your budget for shelving and/or totes. Whatever method you choose it must work for you.
A bit about the batting
In old times our grandmothers had to use cotton batting that was merely carded. It was unrolled very carefully and hand quilted every half-inch to keep the batting from migrating. If you look closely at antique quilts you will see that the batting has lumped into one side of the quilted area.
Our modern battings that are manufactured today are treated with a resin finish or have a "scrim". This special treatment will keep the batting from disintegrating or migrating in the quilt as it is used and laundered.
Each package label will state the minimum distance that quilting lines need to be. Several battings allow you to quilt up to ten inches apart and some only six. Another guideline would be the "rule of the fist" -- place your fist on the quilt. If your fist doesn't touch quilting lines, there is not enough quilting. The closer the quilting the less the batting will move inside the quilt.
When purchasing batting, read the packaging to make sure you are buying the type of batting needed for the closeness of quilting you intend to do on your quilt.