gm. I am redoing the walls of my half bathroom which has a sink and an toilet. There is a small window in the half bath. I want to put tiling halfway or all the way up the wall with the sink and toilet. I was advised to buy 3/8 wonderboard for the bottom and drywall for the top. Which do I put up first the lower part with the wonderboard or the upper half with the drywall?

drywallers always put the top up first so they can get a nice tight seam against the ceiling. the lower piece is cut a tiny bit short and forced up against the upper piece to get a nice tight seam as well. the bottom can be a little bit above the floor because it doesn't matter as much.
this is how the bottom is raised. you can improvise.

Important for DIYS'ers --------

A small gap should be between any drywall or wonderbpard and floor / bathtub / sink etc (Not ceiling or boards of course). This will prevent water from leaching UP into the board and destroying it from behind. The new tile, shoe mounding etc will cover the gap. Without this gap the wall may absorb water - Not good.

For typical 1/4" tile in a half bath, I wouldn't bother with wonderboard at all. I'd use MR drywall.

I have to agree with paul on this one, I would use green board for a half bath, there won't be enough moisture in the air to make a difference without having a shower in there.