I think the wedding ring needs a knife edge binding, not that I know how to do that! But I'm sure you can find instructions if you need to. My mother made me a hand pieced, hand quilted double wedding ring in the 80s and that is how she finished it. To me it just goes with that pattern. Other than that it will need bias binding and I would look for something that matches the background. The pink one could use muslin that matches the background of the blocks or regular quilting fabric, but I think it would look best to try to blend with of match the pink rather than have the contrast of a light fabric. They are both beautiful, you are very fortunate to have these.