Great quilt, thanks for posting that site. Are you doing the straight or on-point version?
If you are quilting it on your domestic machine, and have secured the layers well, you can do the sashing first, then go back & do the blocks. On a long arm, you would normally do everything at the same pass unless you were using different color threads. Make sure that they have a ruler base on the long arm machine that you are renting. This will ensure that you can use the rulers safely.