I use peat moss mainly because it seems to not dry out as quickly as sphagnum moss. I used sphagnum for years however, and it is great as long as you remoisten it daily.
I've never used vermiculite in the layboxes, I always worried about the leos eating it. It probably wouldn't hurt them though, well, no more than eating the peat moss would!
I have used peat moss because of it's availability and popularity in laying boxes but I have since switched to cocofiber and would recommend that more than anything. Its great stuff!
I use eco earth. It stay moist for a few days. It gets really dusty after it dries out though so I try to keep a good Eye on it to make sure it's not drying out.
I use what Jeanne does. Jeanne, did you know that it is commonly sound in brick form (like the eco earth) and expands when water hits it? It easily makes 2 dozen fresh humid hides here. Ask local dart frog breeders for the bricks of sphag moss, it's really cool!