Love this quilt!
I highly recommend that you heavily starch the backing before layering, especially since it is flannel. Heavy starching will stabilize the fabric so you don't get puckers when you machine quilt. My method is to mix a 1:1 solution of Sta-Flo liquid laundry starch and water, "paint" the solution on the yardage with a large wallpainting brush until the fabric is saturated, toss in dryer, then iron with steam. The backing fabric will not stretch or move on you while you are quilting.
It's also a good idea to heavily spray starch the top, for the same reason, to stabilize so the fabrics don't distort on you while you are machine quilting.
Your choice of batting depends a lot on how apart you are going to make your quilting lines.
My favorite machine batting is Mountain Mist Blue Ribbon 100% cotton. This is a thin, antique-like batting that creates a crinkle effect when washed. One of the reasons I love it is because it gets softer with every washing. However, this is a thinner batting than some people like, and it needs to be quilted every 2 or 3 inches.
Hobbs 80/20 is my second-favorite batting. Gives a little more puff but still easy to handle. (High cotton content means the batting will cling to your fabrics to prevent shifting; all polyester battings are much more likely to slip and slide a little.)
Many here like Warm & Natural, which is an extremely stable batting needlepunched through scrim and therefore can be quilted up to 8 or 10" apart. However, the scrim creates a slightly stiffer drape than the two battings I mentioned above, which is why I prefer not to use it. It is also heavier in weight than the battings above. Some people like weight, but I do not.