I usually stitch to the front and hand-sew to the back. The width of the binding depends on the width of the edge in the seam, and the bulkiness of the batting. I do straight grain binding, I'd probably use 2 1/4" folded in half, for a placemat. But normally for a placemat I do by birthing - sew all around the placemat with backing and thin batting, with a small section left open for turning; then I top stitch around the edge, about 1/4 to 1/3" from the edge.
Watch a few tutorials on doing the binding. Once you get the hang of it, the corners are fairly easy to do -- start in the middle of one side stop stitching 1/4" before the end of one side, take the needle up and turn for the next side, fold the binding up to the edge of the first sewn side, put the needle down 1/4" from the already sewn side, and do the same thing with each corner. There are several ways to make the binding match when you get all the way around the placemat or quilt.