Welcome to the world of fiber stashes! I'm not sure they are still available anymore, but I use the Rubbermaid storage bins. They came in two sizes, a 5 gallon and a 7.5 gallon, if I remember correctly. And they came in many colors. What I like about them is
1) they are not see-through so no fading of colors
2) the lids are such that they stack easily without sliding
3) they are roomy inside for most fleece and easy to clean
4) I've never had a moth get in!
5) they are easy to label and organize
6) they have little "breathe holes" under the handles
If the exact type I have isn't available anymore, I'm sure there are others that are close. The one down side to using any plastic is that they MUST be stored where they do not receive direct sunlight. Sunlight + plastic = condensation which can lead to felting of the fibers over time.
Pegg