If you can, I suggest two. They will probably all use the same one almost all the time, but two gives you some flexibility in how you manage them. The obvious need for an extra one is if one goes broody and won't let the other two lay with her, but I find a little more flexibility is usually a good thing. If two is a problem, one will work.
For your breeds, I think 12" x 12" is a good minimum size. A little bigger won't hurt but is really not necessary. I made mine 16" x 16" with the thought that two might want to lay at the same time. Usually they don't but I have seen three in there at one time.
As far as height, it depends some on how you frame it. I like a 5" to 6" lip across the bottom to keep them from scatching out the bedding and eggs, then leave a 6" to 8" opening above that for the door. 6" does not look like much but I have used that successfully for the opening height.