You do not have to make a big SNIP as I have shown in the pictures, I only did it that way to show you where to make the snip, always make certain it is on the very outside where both fabrics meet - I always had to think about this before I made my snip on both fabrics.
Yes - sew the borders together first, then add to the quilt. DO NOT sew the borders tight to the corner of your quilt, stop a couple of stitches before the corner on the quilt, and be certain to tie off your threads at that quilt corner.
I know you will find this alleviates any puckering at that point. This is the easiest method, without any calculations.