What size should I cut my backer board?
The reality is that it doesn't matter all that much, and optimizing for whatever allows them to reuse the most material or minimizes cuts should be your first priority (I see you have another uncovered wall that you might want to factor in).

That said, if you are sure you only want to cover the area stated in the question, then it would seem you are in for 2 pieces of backer board no matter how you slice it.  Thus, you might consider cutting boards twice so that you will have vertical seams for drainage reasons.