When I first started quilting i took a class on Scrap therapy at our LQS. There is also a web site
www.scraptherapy. I also read BonnieH web site on scraps. I have combined my storage and processing of scraps using both methods. As crartterrin1 has said find out what is going to work for you. As I work a project, I cut down strips for future projects on small pieces. Anything more then a fq I do not cut up unless it is a color I use a lot of. when I'm piecing any cut offs or left overs go into a small basket (plastic 6 x 8 Inches or so). When i have collected a few baskets and when the mood strikes me, i will sort by sizes and put in proper drawer.
I go to my precuts constantly when I only need a little bit of fabric. I make a lot of table runners, and sort of scrappy quilts. It sure saves getting out a larger piece of fabric to cut a small piece off
If this helps the following are my chosen scrap sizes:
2" sq, 21/2" sq, 31/2' SQ, 5" sq, 2" strips, 21/2" strips, 3" strips, 4" strips, 5" stips, less the a fq folded, less then 2" strips, finally corner clippings, thread clippings, salvages etc into a container to make dog beds. As I cut off bindings I sew 1/2sq triangles for future projects or make pinwheels if there are enough projects.