Marion,
I forgot to mention the stitch. Do you still have the brother machine? Look at the utility stitches on the first page. There is a zig-zag that drops down instead of side to side. It may stitch # 1-06. You can shortened the width/length settings and get a finer stitch to go around the smaller pieces. Play with the width & length of this one. Make some samples of them on a scrap sandwich and mark with the settings.
I have been adding a light-weigh fusible to the background fabric for applique. It helps prevent puckers around the pieces. Pellon 101 works well.
Good luck on your project!