Ditto for me.

I fold my binding in half, sew it on the front, never have used a walking foot, just my regular 1/4 " foot, no matter how thick my batting is and then I stitch it down by hand on the back. I guess when you don't know any different, it always works!

I have a walking foot that I purchased somewhere around 1996 for $25 and it's the best investment I've ever made for sewing. I keep it attached to my Singer 237 or 239 (never can remember which one) that's in a table all the time and use it for straight/slightly curved quilting as well as bindings.

Without a walking foot I would stitch around the quilt a little less than a quarter inch from the edge. Then I would sew on the binding increasing my stitch length. I have sewn on many bindings without the use of a walking foot. You'll be fine!