I use the plastic boxes for my storage. Looks like you have some of the clear Sterilite boxes already. I use the shoebox sized boxes for projects in process and then supplies - and label them on the side that wil show. I use the next size up to store my fabric. I fold it and put it in so that the fold shows against the side of the box. This way, I can see what colors I have. I use this for yardage up to 2 or 3 yards. Larger than that, I put on a hanger.
I don't know if you have a closet in the room, but you might want to put shelving in a portion of the closet. I plan to do this with my closet using the Elfa system from containerstore.com. It's a little pricy though (but currently 30% off) but I've seen similar shelving at Home Depot by Rubbermaid. The nice thing about these systems is that the shelves or clothes rods hang on tracks that are suspended from a horizontal track that's screwed into the studs up by the ceiling, meaning nothing on the floor.
The systems are adjustable so you can move shelf heights as your needs change.
Good luck. Being organized will feel so good.