I have made a few string quilts. I have done some with muslin, as the foundation - those I did not put in any batting, just quilted top to back. Also have done some with old phone books, as the foundation - took some time to tear out, but the phone book was free. But the foundation that I like the BEST - the super light, see through fabric that one can read the newspaper through (a 'friend' gave it to me).
String blocks can be ANY size you want them to be. I usually like 8 - 11 inch block. As far as the size of strings, Larger then 1" - smaller than 2.5", IMHO, it is more interesting when they are of various sizes. I have seen them with about 3" strings, not my cut of tea. They DO NOT have to be perfect rectangle strips, wonky is okay.
As far as organizing your scraps I agree with MadQuilter, check out Bonnie Hunter's "Scrap Users system", her blog:
http://quiltville.blogspot.com/ then go to Tips and Techniques, where you will scroll down to "Scrap Users System.