I have done a variety of mug rugs over the years and I don't care for the satin stitch edged designs. My preference is a bias binding, as in a quilt.
The one thing I like to do is to use a flannel backed plastic tablecloth for the backing, or at least the inners if I use a matching backing. The flannel is soft and the plastic makes it waterproof.
As I said in a previous post, I'm not doing much embroidery right now, so this may be old information!