Where do you live? I have never had a problem with mustiness in my stash, but a great deal depends on where you are storing the fabric. If it is in a damp basement, then you do need to take extra measures. I have not had to deal with damp basements, so my stash has been fine for many years stored in plastic totes.
For plastic totes, I highly recommend getting the ones with clamping lids, as they keep mice out and also the lids do not distort. Of my totes with lids that do not have clamps, some of the lids have distorted over time and are not really secure anymore. In my opinion, the clamps are worth the extra money. I also think it is worthwhile to get totes that are see-through in the lid as well as the body. Here is a link to the general type of tote I like:
http://www.walmart.com/ip/20699702
This size tote is good for batting, but filled with fabric it would be way too heavy. Here is my favorite for fabric storage, although it is no longer sold
:
http://www.walmart.com/ip/20699641
If you use rice to absorb moisture, I think you definitely will want clamps on your totes to keep mice and bugs out (assuming rice is attractive to them, which I don't know for sure). Instead of rice, you can purchase silica gel at JoAnn's or Walmarts (usually in the area where the artificial flowers are) and make up your own packets. Youtube has some videos of hunters who make up packets using silica gel and paper towels to place in their ammunition and other metal boxes to keep moisture away.
If you have a damp basement for storage, I do think it's wise to invest in a dehumidifier unit. Moisture in fabric is primarily what causes the musty smell.