The uncut ones, I have in paper boxes for now, probably not the best storage idea. I usually cut the biggest square I can from the piece and then work downwards. The smallest I cut is 1 1/2 inch squares. Then I have put them in the clear plastic storage boxes by size. Strips I cut anywhere from 1 1/2 inches wide to 3 inches wide if there is enough material to go three inches. I have those all together right now in one box as I don't have too many strips yet. May change the strip storage as the amount grows. Plan to use Bonnie Hunter's Leaders and Enders on some of them and who know what else on the others, but at least I am getting them cut into sizes to be used in the future and not just a box of "junk" sitting around. Have several boxes full that need attention and once I get my sewing room more organized will work on them.
My sewing space room will be full up so to speak, with room for me to move around the cutting table and sewing machine area, but figure no one will be in there basically but me so that is fine. Have a long way to go on organization and it is basically being put off until we finish moving completely.
Made a small curtain for a small window to break the afternoon sun in our faces yesterday and it is going to work out fine, so need to do a second one for the other small window. It was so nice to be able to work and not have to move everything when I was finished and just close the door. Loved it so figure eventually I will get more sewing and quilting done.
So find what works best for you, I like the clear boxes as I can see what's in them, but I also label them too, as sometimes some of the sizes are a little difficult to tell from the end of the box.