Right now (which is just about to change) I simply hang my fabrics on a mulit-tiered clothes hanger.
I got a few of these at Bed, Bath & Beyond. Cost like $7 or so per hanger. Each hanger has 6 rods. Downside - can't eyeball the fabrics as easily as I would like - but it takes up little closet space overall.
I used to use this type of plastic 3 drawer cabinet I got
But it was stuffed to the the point of not being to get the drawers open. So that little cabinet has been relegated to serve another storage task.
My friend Cindy uses these:
Which she stacks in the corner behind a door & arranges each bin by color mostly. She prints off a little label that she can change out when her fabrics change stating what type & how much fabric she has in each bin. She has 8 total bins - 2 columns of 4. The clear bins let her eyeball what she has & the bins are easy to handle. She has a LOT of fabrics too. Bulky stuff too like boucle's.
My friend Charlene uses these:
She hangs each fabric on it's own skirt hanger. Now she also has a whole closet rod dedicated to these suckers in a whole room dedicated to sewing. Almost want to hate her!
I'm digging the filing cabinet idea - I like when things are close by but out of sight. That sounds like my kinda of storage.
Hope this might give you some inspiration. Jane