I've found what works best for me is to have containers labelled with different sizes of blocks, strips, etc.
Then as I work on a project and am done with that fabric, if it's too small to be anything more than a "scrap", I'll cut decide if it's long enough for 2-1/2" strips (meaning at least around 12" long to make it worth it), then cut the largest square I can get and work down from there. I have a separate (small) bin by my cutting table that I just toss those scraps into. Then when it gets full, these get sorted and they go into appropriate container. My squares are labelled with 2 - 4 inch squares since these work pretty well with each other. I don't sort by color.
Then, as I'm working on a regular project, I have some of these scraps near my sewing machine and use Bonnie Hunter's Leaders and Enders method. This starts working up into a nice scrap quilt quickly.
Hope this makes sense.