Someone said the most successful scrappy quilts are willy-nilly, however I think it's a matter of quilt design and personal preference. I made a scrap pineapple quilt that was not "willy-nilly", I split my fabrics into lights vs darks and the contrast turned out quite beautiful. The string quilts I've seen that I thought most striking were either completely scrappy ones that had a unified center line throughout all of the blocks, or had some sort of design element such as fading from dark to light, or red vs. blue, etc. Again, however, it's a matter of personal preference - and what type you choose to make will determine your course of action regarding how you manage your scraps.
If you haven't already, you might take a look at the scrappy quilts pictured on this board. They might give you inspiration to make one, then you're off and running with your own ideas!
http://www.quiltingboard.com/main-f1...s-t187228.html
http://www.quiltingboard.com/members...bums16956.html