The first sphagnum moss I tried to grow I used a substrate of peat moss. The humic acid and tannins wreaked havoc on the green sphagnum...staining the sphagnum with brown ugliness and seemed to retard the sphagnum's growth until it dwindled away. Now, this was my first attempt so there was probably something else I messed up on, so take that experience with a grain/chunk of salt. The next few batches that I've started I simply used an empty plastic container five or six inched deep and something like 12x18(?) in size and scattered the moss out on the bare plastic bottom. I watered it enough so that the bottoms of the moss were in water but the tops were out. No brown staining and the moss has done much better. I had plenty of moss to start with, though, and it wasn't scattered out too widely so that may have given me an edge, too. Since that first time, though, I just haven't wanted peat beneath my live sphagnum.
On another note... I have thought about starting a layered substrate to try growing on. Starting with a thin layer of silica sand, then a layer of a mix of something like 75% silica sand and 25% peat moss (maybe), then a layer of dried sphagnum, and finally the live sphagnum on top. Semi, kinda, maybe replicating a native substrate. It's probably more trouble than it's worth doing but I may just try it. I'm sure I'm inventing the wheel here, but I might as well give it a shot one day.