are you doing beadboard (tighter vertical lines) or something like board & batten (wider vertical lines)?

We have beadboard and I believe it is 36", set in a 2.5" base + 2" cap moulding.

I haven't decided the width of vertical lines - but I do want PVC beadboard (as this will be a children's bathroom and lots of potential water/splashing right next to the tub area). The PVC beadboard will likely dictate the width.

I thought it would look best if the beadboard went past the towel bar, rather than underneath it...??

to clarify - the total 54'' from the floor - this would include baseboard/bottom trim, beadboard, and caprail.

Another question - If I am planning to repaint the bathroom walls, is it best to prime/paint the walls before or after the beadboard is installed??

Paint after, because you'll want to cover the caulk with paint. Otherwise it will be sticky enough to catch dust.

I'd paint before the board, then touch up as needed.

I would do the height of the shower and paint the headboard white. Paint the sheet rock above a different color.

your bathroom is almost the exact same as ours-ours is a bit smaller, I think, based on the size of your vanity. I'm planning to take our over the toilet cabinet out and put up a few shelves w/baskets.

Here is an older thread with some nice pics in the replies to give you an idea of scale. I prefer the lower wainscot. That is my personal preference and may not be yours. Taking bead board high in the room makes it look more like wall paneling. But perhaps that is the look you prefer.
[https://www.houzz.com/discussions/wainscoting-height-in-small-bathroom-dsvw-vd~3514185[(https://www.houzz.com/discussions/wainscoting-height-in-small-bathroom-dsvw-vd~3514185)

Here is an older thread with some nice pics in the replies to give you
an idea of scale. I prefer the lower wainscot. That is my personal
preference and may not be yours. Taking bead board high in the room
makes it look more like wall paneling. But perhaps that is the look you
prefer.

This is a picture taken from that other thread, and -- yes -- I do prefer it higher. Additionally, it would allow you to match the top of the bead board to the top of the shower enclosure /top of the shower curtain. I like that it allows for a small picture rail.

I like it higher like that as well.

I think it might depend on two things: the age of your house and your decorating style. If your house was built in the 1940s or earlier, you can go high. If you are more country in decorating style, you can go high. If you are cottage in your style and the house is semi-old, maybe you can go high. If your house is newer, stick to the height of the backsplash. The room is too small to have the top rail not lining up with the top of the backsplash.

All my own personal opinions, of course!