Use a "textile spray adhesive," like 505 spray. It holds the layers together very nicely, then washes out. I've worked with Minky on my home machine and also on my longarm, and haven't had any problems. After you spray baste the layers together, sew a basting stitch all the way around the outside edges. Use a walking foot if you have one. You may also want to use a few safety pins.
Self-bindings are actually harder to do on a machine quilted quilt, because you'll probably want to square-up the edges when you're done with the quilting, and won't be able to. For me, it's a lot easier to put a traditional binding on. If you're binding with Minky, you don't have to turn the edge under, just sew the raw edge to the front with a serpentine stitch.