Not great air circulation, but cheap:
What about clean, new, garbage cans? A sample of each material and it's measured yardage could be stapled to a card, and taped to the lid. Maybe some kind of drying agent could be put in each can.

I store my trims in an old file cabinet.

Not so cheap, but good ventilation:
I store most of my fabric on a wire shelving unit, but it's in a big closet that doesn't get direct sunlight. I purchaced the units at Bed,Bath, and Beyond, but since then I've seen similar at Target.
If you ask around, people you know may be getting rid of old dressers or containers. Any time I've helped any one move, I've come home with *something* that he or she couldn't use anymore and was going to the dump.

I'm not a cat owner but I've heard that kitty litter is a great odour and moisture absorber. Maybe you could sew little bags (like sachets), fill with litter and tuck into your storage containers. It's cheap enough and might be worth a try.

I vote on garbage cans & kitty litter too. Garbage cans for large things that you won't be going into often. The small things that I was considered heir to have been gone through & seperated into catagories & stored in gallon zip lock bags. I have lots of zippers that I stored by lengths & by lights & darks. Before I run to the store, I grab the appropriate bag & check first. I had tons of invisible zippers from the last time they were popular. It is amazing how many of those I have used lately ...especially after reading that you can doctor up the pulls to match current colors with nail polish. The tape doesn't show, so it doesn't matter what color it is.

A few years ago I lived in an area where the basement sometimes flooded just an inch of water. I used the plastic trash cans for clothing storage and the items never even smelled slightly off. Just make sure your items are very dry when you put them into the trash cans - maybe use the dryer for a few minutes to completely dry out the items. Also, DO NOT use any plastic bags. That traps the moisture inside. Good luck,

yes make sure they are well dried before storing them anywhere, wash and hang the already spotting ones in the sun. sometimes lemon juice will take out mildew stains. They need to be stored in something airtight.

Look into the reasons your house is so damp too, dampness and mildew is not good for the health. My daughter was constantly ill when we lived in a very damp house that the owner would not do anything about, they had moved out because the husband was constantly ill.

If you have small notions, one of the things I did might be workable for you. Like you, I became heir to my hubby's grandma's assorted 'goodies' (buttons and the like). I went to Home Depot and found one of those large, somewhat transparent, white plastic compartmentalized containers (they look like Tupperware sandwich containers with separated compartments) and I sorted all the buttons, trinkets, fastenings, etc. It was a calming activity to do while DH watched TVÂand now, all the little things are neatly sorted and easily accessible! At HD these things are where they have nails and toolboxesÂ

There's also this store called Harbor Freight where they sell an assortment of 'goodies' that are much less expensive than at HD. I'd found the same plastic box at HF for WAY cheaper.

Here's just an example of something you could use for notions.

Here is a link that might be useful: Link to Harbor Freightone notion storage idea

I would certainly wash and dry all the materials before putting them in storage. It should stop any spotting, perhaps remove it before it sets. If you can't get the spots out, do you want to keep that stuff? There might be material you hate, will never use, get rid of it now. Don't bother storing it.
The garbage cans sound like a pretty good idea for big quantities. I bought the Rubbermaid tubs, they fit my storage areas, stack well. Do a good job of protection from moisture and sun. Very tough containers.
I have heard that if you ask at the pharmacy, they will save those dessicant packages that come in pill bottles. You can put them in stored material for drawing moisture. They can be reused if you dry the packs out in a very low oven.
Other folks ideas sound pretty good. I also would get a dehumidifier, find out why everything is damp all the time. Mold would also be a concern for me, creates breathing problems.

I have my sewing room in the basement and have stored my material on bolts from the local fabric store. I place the bolts in boxes according to the type and cover them with old sheets. The wool I keep in plastic storage boxes. The thread I keep in plastic ice cream containers. I have had no problem with the working in the basement. I do keep the little bags that come in purses, clohting and so on and place them with the material.