Okay, I'm actually giving advice without having done this, but...
I think it would be much easier to do your machine applique before you add the backing and batting. Since it's a wall hanging, you don't need to do much quilting, so you could just do the machine applique, then layer the piece, tack it down in a few places, and be done. You could use the birthing method if you don't want to bind it. Personally, I like the look that quilting gives, so I would probably quilt it - a lot.
I meant to add that it will make a lovely wall hanging, any way you choose to finish it.