You are right, zozee...trimming as I go works best for me as well. Any more if it's smaller than a FQ it gets cut. I do like to keep chunks of widths of fabric that are suitable for binding on table runners or mini quilts intact...think fabrics that read solid...browns, reds, blacks etc.
MsMorgan as you are a new quilter...figure out what kind of quilts you like. Do you like scrappy, controlled scrappy, or not at all? Will you make table runners or small wall hangings? Answering these questions will help you decide what kind of system you want to use. zozee has a good suggestion on mixing colors until they get a bin of their own...kind of like roommates!