I don't have problems with bugs and I keep my large stash sorted by colors or themes in cardboard "banker" boxes I get at the office supply store. I can't always afford archival boxes but it is worth paying for heavy duty boxes which I then line with acid free tissue paper. Some of my fabrics I've had for many years and I like the light protection cardboard gives. Cardboard however should never be put directly on concrete floors, it will wick up trace amounts of moisture leading to musty smell and attracting critters from mold to mice. I have rolling wire racks I got from Costco that by boxes are on -- my goal for this year is to clear out the large closet in the sewing room and put in a shelving system and I believe what is (left from my formerly huge stash) will fit in that closet. So although it is 1/4 or less of what I used to have, it's still a sizeable amount. I write on the outside of the box what the color/theme is --or why a lot of people like clear storage.
There is no one answer, each of us find things that work. I've tried many things. One thing I've given up on is small pieces, for me that is anything smaller than 6.5" x something bigger than a square. Pieces fat quarter and up are prewashed, sorted by color or theme (cats, farm, blue, red, etc.) and are folded in fourths ready for cutting, they fit well in the boxes that way.
When they get smaller than a fat quarter, I cut off a 6.5" strip which I keep in a 6.5" strip box. I used to keep smaller strips, but although I can cut down I can't make them any larger and it just wasn't working for me. I used to keep the rough cut strings. I used to do a lot of things I don't do any more... Now I keep a flat rate postage box by my cutting area and anything too small for me goes to a crumb quilter I met on the board, when it gets full she gets a surprise box. A lot of it is bigger than a crumb -- but again, she can cut down and I can't cut up!
Final thought -- I work mostly in scrap quilts or at least quilts made from collections of fabric. But after a lot of years I have my own style and still find a lot of scrap quilts to be too chaotic for me, or some fabrics just don't speak to me in ways they can be used. So I've started examining why I save or use/don't use particular fabrics. If you think about it and realize that no, you just aren't ever going to do something with the fabric you don't have to keep it, you don't have to use it. I think it's better to give it away/donate it but what the heck. A lot of people are just happier buying a lot of fabric and making a project and they don't need the leftovers. I'm happier having a lot of fabric and figuring out what to do with it.