Obviously, not everyone has enough room or resources to store quilts like a museum! Here are some options for you to consider:
Shelves: I had this closet built for quilt storage with larger than average shelves so the quilts could be folded less. The shelves and the walls were painted with a polyurethane varnish to block any oils from the wood. There is a vent in the closet for heating and cooling circulation. I also have non-chemical pest control (glue traps).
Pillowcase (on a closet shelf is best). Make sure the pillowcase is large enough so the quilt fits without having to shove it in. You will still need to take the quilt out to re-fold on different lines every 3-4 months.
Protected, enclosed area: Here is a photo of one of my storage areas, my armoire. I take the quilts out frequently for programs or display. Yes, you still need to re-fold the quilts on different lines every 3-4 months. I also switch the position of the quilts so that each one only spends a short time on the bottom of the pile.
Plastic containers: I use polypropylene containers (Sterilite mostly). You can identify this type of plastic from the recycle symbol. You know the rest - don’t pack the box tight, refold regularly, switch bottom quilt to top.
Trunk: Not a cedar chest!! I don’t put fragile quilts in here.
Rotating the quilts and refolding is very important if this is your storage method.
Bed: Hey, here’s an idea: store your quilts on a bed!! You can stack several.
To avoid light exposure, cover them with a bedspread. Of course, this is only practical in a bedroom that is unoccupied and protected from two and four legged visitors.