I store yardage over hangers in the closet. I color group it to make it easier to find things. Smaller pieces are stored on shelves on the wall in plastic boxes. By being on the wall, it leaves me more floor space. The downside is that I do have to use a small step stool to reach the upper boxes. I color/theme sort those to make it easier to find what I need and all boxes are clearly marked using mailing labels and a sharpie. I also have the shelves away from the windows and light so there is no fading.
As far as washing goes, it might be best to wash it. You could do a load every time you wash regular clothes or whenever you have time. I wouldn't bother starching and ironing until you're ready to use it. When I buy new fabric, I usually don't wash it, but I do a lot of wearable art jackets that won't ever be washed so I'm not worried about shrinkage or fading