Machine binding is usually faster and stronger. A few suggestions to make it easier.
1. Make your corners round. Just lay any circular item on the corner and trace around it. A saucer is a good size. Stay stitch the new line then trim off excess.
2. It takes a few minute longer but bias binding is easier to apply. It will go around the new round corners very nicely. Be sure to sew it to the back side first. I usually cut mine 1 1/2 wide so it's easier to handle. I use long superfine quilting pins to pin the folded edge of the binding just over the stitching line. Put the pins in perpendicular to the stitching line every 2-3 inches.
3. When stitching this edge down go VERY SLOWLY. It's much easier to control the line, and you can poke the edge in place as you go along with a sharpened skewer.
My machine has a double cross stitch that works nicely.
I just did a baby quilt last week that everybody is raving about. Good luck and remember to slow down.