I think you first have to define what size of fabric you consider a scrap and find a method that works for you.
My scrap fabrics are different sizes and stored with different methods.Some are plus or minus a FQ size. Those are ironed and edges trimmed neatly. Then ruler folded on a 5 inch ruler. These pieces are stored upright in a plastic bin. Easy to pull out a specific color or pattern.
Smaller pieces or strips are sorted into smaller plastic bins. I started sewing 2.5 inch strips for mindless sewing. I have no idea how they will finish into a quilt or project. LOL.
There are times I play with the accu-quilt and simply cut scraps into squares, triangles or strips. Just depends on the mood.