I would say if you are going to use the fabric for quilting or piecing projects, 1 inch would be easiest to handle. It will yield a 1/2 inch pieced piece. I am currently using 1/2 inch pieces in a quilt as you go project, but I am not piecing those, I am tacking them down with decorative stitches. If you can find alternative ways to use the scraps (as many have mentioned), then you can really save anything. But for piecing, 1 inch is probably good.
Cheers!
Rachel