I buy cardboard "Banker Boxes" from office supply stores. The best are archival quality, but that's usually a budget stretch for me, so I buy heavy duty and line with acid free archival quality tissue paper. The lighter weight lids do not last well, heavy is the way to go.
The boxes are a consistent size, and that size fits prepped fabric very well! That is yardage folded in 4ths across the width. You can stack them easily 4-5 boxes high. While a full box does get heavy, weight isn't too much of an issue. I still have a few pieces of fabric that I bought in the 70s/early 80s, along with vintage fabrics, and light protection is a concern of mine.
I sort by general types or colors, so I have a dark blue box and a light blue box. I have a box just of cat fabrics. I have other color or theme boxes, some 23-26 total... I just write on the outside of the carton "Green" or whatever it may be and make sure to stack with the color name facing out. If I change/reduce my fabric, I write the current contents on a piece of paper and tape it over the old name.
It is very important if you store in cardboard that you have no issues with bugs, and that you never ever store cardboard directly on a cement slab floor. If will wick up trace amounts of moisture and you will get the musty smell and it will attract critters. Even though my sewing room does not have a cement floor, I keep my boxes on rolling racks so they can get air flow.