You can't go wrong with hide glue for rawhide. CA glue for the antler tips works well. Not sure if its the best method for backing, but moistening the hide in warm water, starting near the tips with a clamp, stretching the hide as you put it down, squeezing out air bubbles as you go is pretty standard...
I'd use whichever of those two choices for backing that is the thinnest, you don't necessarily want the extra weight of thick hide on there.