Depending on the size of scrap, I'm tempted to cut all my scraps into 5" strips, or if too short, cut 5" squares (nickles). If they are all a similar size, they would be so much easier to store. They would be easy to sub-cut into 2 1/2" strips or squares when/if needed. The trouble I seem to have is making the time to do it. I think that size would be fine for most applique, right? I know there would be a few pieces larger, but not usually a lot.
If you don't really want to use totes or bins, how else would you neatly store your scraps? I use clear plastic shoe-box sized storage for my fabric. I fold it in half length-wise and then roll it around my 6" ruler. It fits perfectly in the box, the boxes stack nicely on the shelf, and I can see what's in them.
There are so many ideas of how to store fabric, but scraps do me in.