Scrap quilt blocks tend to be "busy" with all the different fabrics being put together. Unless you like the busy-ness, it is necessary to calm things down. How do you do this? By strategic use of a solid fabric. The solid fabric gives the eye someplace to rest as one studies the overall design of the quilt top.
Makers of old scrap quilts used muslin as their background fabric. Some chose a solid coordinating color fabric for the sashing between their scrappy blocks.
Unbleached muslin, white and black are all good solid fabric choices. Audition each against your scraps to see which one shows off the colors in your blocks the best. If there is a predominant color in your scrap blocks, perhaps that would be a good solid color choice. Other colors to try in sashing, borders or cornerstones are teal and brown.
Lay out your blocks against your chosen colors, either on the floor or on your design wall. Stand back and study the layout. The color choice(s) will become obvious. (If you find that you need to shop for your solid fabric, be sure to take all of your scrap blocks to the store with you. Find a spot where you can lay the blocks against several colors, stand back and decide. Again, the color choice should become obvious.) How satisfying to find just the right color to show off your scraps!