I recently installed a closet organizer system and now use 3 drawers like this. My longtime goal to have this after we moved into our forever home. But prior to that I used the plastic bins on the right of the picture. And before that I used canvas shoe bags (all sizes) and stored by color. All 3 worked, but I found separating my fat quarters from the larger pieces is much more useful to me now, but it's clearly a personal preference.
I plan to use the empty plastic pins to store projects. I attach a card on the outside.. keep everything related to the project in it so I can keep things organized and switch to work on one project over another easily. Or take one with me on a trip as we sometimes do . I also use 12x12 plastic bin to store scraps by color. I started storing scraps in baskets when I worked on a Civil War project and soon it was overflowing and switched to the cases and they hold more and easier to store. Now when I get down to scraps I just throw them in the proper case.
I spent over a week organizing my fabric before we moved into our final home. Cutting and folding fat quarters and larger pieces onto comic board backs. It was exhausting to do, but I am so happy I took the time.
Interesting thing I found @ a local quilt store -- they rolled their fat quarters and secured them with rubber bands. I found it a bit difficult to tell what they were stacked in so tightly as you only saw the end of the roll, but they did store them by color. I have a pile of blue FQs in the red bowl on the bottom shelf in picture above that I used til we had moved everything to the new house. Just haven't taken the time to fold them properly.