The first thing to analyze, tk, is what type of quilts do you like to do. Me ...I make miniature quilts, but only use scraps..so I have small bins of individual widths and will sort these into lights and darks or even particular fabric styles like brights or CW repro/Kansas Troubles. For this mini I pulled a cream and red strip from my 1" bin and went to the 2 1/2" one for the border and binding. I did cut the 4 setting triangles from a larger piece.
The same concept would apply to larger squares and strips. Do you gravitate toward jelly roll patterns? Then save 2 1/2" strips.
Do you like string quilts? Then exact widths may not be an issue for you
Can your scrappy quilts be random or do you like to control the color placement?
Personally I don't cut a large chunk into smaller pieces...that large chunk may be the perfect size to cut setting triangles in a quilt like the one above. Those chunks are sorted by roygbv, black, brown, white, cream, gold, and tan. Holiday scraps, pastels and brights are kept separately
Decide what your habits are and go from there...as I get lost in a sea of scraps. Currently I pulled out all my blue and rose colors along with creams to make the online 365 Australian challenge quilt with the intention of using the smaller chunks first if at all possible. Good luck...