How thick should my tile underlayment be?
When I did this in my old house I had a 3/4" subfloor and used 1/4" backer board (with 1/4" notch thinset between the subfloor and backer). I don't think that direction matters given how many fasteners you'll use on that backer board. Don't neglect to tape the joints either.

That floor never moved after adding tile on top.