I personally like porcelain tile for floors like a mud room or laundry room. Porcelain is strong and in many beautiful colors. Luxury vinyl tile would work too and there are many looks for that too. I would not use wood or natural stone. Wood because of abrasion from dirty feet, and stone because you need to be sure the joist system is strong enough, might be an issue with your new build specs. Floor joist have to be rigid for porcelain too but not has stiff as with stone.

I think brick will have to be dusted and collect dust easily. Just my opinion. I have seen brick tile for floors that might work for the wall. Sunderland's has them I think.

Thank you for sound advice. The last thing I want is to be dusting a wall ! And the porcelain flooring seems like it would be durable, easy to clean and beautiful.

With the tile floor be sure to follow the North American tile assoc guidelines. I’m not sure it that is their actual assoc name or not. You won’t be putting tile directly on the subfloor. You’ll need a decoupling membrane such at Ditra, then the tile. Cement board is not structural, so if it is used, it won’t add strength to the floor, just a surface for the tile. The strength comes from the hoist and the subfloor. Cement board is not sub flooring. John Bridge forum has loads of info on tiling.