Edit: I forgot to add the quilting part.
I just did Stitch In The Ditch around the star and I sewed along the inside edge of the border. You wouldn't have to quilt it down I suppose but I always like to.
When you sew the inside of the border make sure you don't push the border into a scrunched up mess at the corners.
If I have a problem with one I sew from one end to the middle and then sew from the other end to the middle so you can keep the fabric evenly spaced out. If you get a spot that the fabric gets a little overlapped you if the spot is not too much fabric you can sometimes use your fingernail and scratch it til you get the fabric to smooth back out
Of course if you prefer to do straight line sewing across the hotpad or any other type of quilting that is entirely up to you.