Just happened to see this. I did (what I think) is a pretty nice board and batten style wainscot in my master bath. I attached a pic where you can see the style along with a vanity I built. I used MDF for the panels and poplar for the rails and styles. I affixed the mdf to the wall with construction adhesive and placed the edges on studs and nailed. I then laid the rails/styles over it to cover seams. They rails/styles were pre-assembled using pocket screws then laid over the mdf and nailed at the studs. I know some may frown on using MDF in a bathroom but primed, covered in two coats of latex, with the edges hidden it's really no problem. The MDF is also super smooth, takes paint great, and is way cheaper than plywood.
First off, BEAUTIFUL WORK! Both on the walls and that vanity, really nice!
After lots of debating, I decided to go ahead and sheetrock the wall, and decided I'm going to then put 1/4" over it. A lot of people kept saying to put the rails and stiles directly on the sheetrock, so I figured I'd just rock it all, and am then going to put 1/4" of something on top. Home Depot had a nice piece of 1/4" Birch for around $28, so I think I might go that route. They have 1/4" MDF but i'm going to decide one and roll with it.
For your Rails and Stiles, what is the thickness, both in depth and width? I see people recommend anywhere from 3/8" up to 1" stock. I don't like when it gets too thick since I'm not using a molding on the inner sides. I'm considering somewhere in the neighborhood of 5" for the bottom rail, 4" for the top rail, and then use 3" vertical rails. Any dimensions (Thickness Depth and Width) you can share on top rail, bottom rail, stiles, and baseboard height will be helpful
For Rail and Stile stock, Home Depot has 11/16" X 4" primed MDF boards that a few tutorial DIY people on the web have used that I was considering also. The Poplar around here for 1" I think was around $1.85lf, the 11/16" MDF was about $1lf. I'm not covering a ton of ground since the bathroom is small so the cost difference won't be extreme. Is the MDF ideal since it may shrink/swell less?
I finally got all the sheetrock hung last night in there, amazing how much time a small bathroom can take when you bring it down to the studs and need to re-insulate, shim and add studs, get electrical in order, move plumbing and venting, etc. Thought I would have been done by now....lol. Should have known better, I've been doing this a solid few years.