How heavy do you plan to quilt it, and how much do you want the quilting to show? Because it's a wall hanging, I wouldn't worry too much about natural vs synthetic fibers for use and wear - so the quilting I think will be your biggest determination of what type of batting to use. Thinner natural fibers (like Warm & Natural) are not very high loft and don't show the "puff's" of the quilting as much as a higher loft polyester or poly blend. I wouldn't waste money on some of the more expensive battings like wool because it's wall hanging (unless you have a piece laying around). I'm not sure which kind of batting will hang better, but I'm guessing poly or poly blend.
As for hanging it, it depends on what you intend to hang it on.
Do you want to insert a rod through it and hang the rod with rod hangers showing? If so - you can make a sleeve that runs the length of the top.
If you don't want the hanger to show, you can make two triangles that are sewn to the two top corners and leave the bottom ends open (use squares and fold them so the bias edge of the square is folded, and the raw edges are sewn under the binding). Then you insert a wooden dowel under the two triangle "sleeves" and position the rod on a hook or nail in the wall.
You can also sew loops or rings to the top of the quilt and run a hanger though these. Again, in this case the hanger will show on the wall so pick a pretty curtain rod with decorative ends ... or a "quilt hanger".
Google search quilt hangers to see lots of different kinds.