Satin stitch is a tight zigzag. You can use any stitch around an applique. My machine does a nice small blanket stitch. I usually use that. Other decorative stitches can be used too. I've done some with straight stitching and they look ok, but I don't care for it as much that way. Try out some samples to see what you like best.
I use stitch-n-tear stabilizer behind the fabric. It gives a nice look without puckering the fabric, which usually happens to me, especially with a satin stitch.