...not to overwhelming if you do a little at a time!
Set aside a little time each day if you can - and start ironing (which I find relaxing!).
I've got plastic containers - see through - and have cut up smaller pieces of fabric into 4 inch squares, 5 inch squares and 6 inch squares (depending on size of the fabric) .... nice to have them separated by size. The larger pieces of fabric - I've folded and wrapped around foam core board - like mini bolts and store them in a storage cabinet (book case would work too).
There are probably a thousand different ways to store fabric...mind works great for me - hope you find something that resonates with you and go for it!