What are my options for finishing cross stitch ornament edges?

I would like to make several round ornaments with counted cross stitch designs & fabric. But I don't know what to do with the edges. I don't have a sewing machine, so fancy stitching is out of the question. (Well, I have a hand-held sewing machine that does a plain straight stitch.) How can I have nice, secure, and 'polished' looking edges on a circular ornament? I don't want the edges to fray or look too "home-made". I was considering somesort of ribbon edge or matte. I'm a beginner & would appreciate any/all suggestions. Thank you!