Not long after I joined here (and read so many amazing tips), I invested in a walking foot for my vintage machine. It is a very useful thing indeed. I even leave it on for piecing. The binding will go on very smoothly if you pop your walking foot on. By the way, when you are ready to handstitch the binding to the back, here is a link to the ladder stitch technique, posted by one of our kind members.
http://www.quiltingboard.com/t-40083-1.htm