I store my fabric in clear plastic bins, the 27 qt size, not gigantic ones. I've used them for over 20 years and have never had any problem at all with mold, mildew, dampness, fading, stale smells, etc. I am frequently 'in' the bins so they don't just sit around locked up all the time and I also keep a desicant packet in each one to take care of any potential moisture problems. My system is ideal for my space and the way I work.
There are so many different possibilities for fabric storage it can be daunnting, but you're sure to find a solution that works well for you, your fabrics, and your method of working.