If you have the wainscotting white, it will blend with your fixtures. Just don't choose a white that's brighter than the porcelain. If you would like grey walls, go with a blue-grey to give a 'sky' effect. Sherwin Williams SW 7662 EVENING SHADOW or SW 7663 MONORAIL SILVER would be good options. You might even paint the ceiling the same grey-blue colour for a nice effect.

If you are looking for a more dramatic change then go with grey wainscoting.

Small room. Pick white for woodwork. Wainscoting is great looking! White for walls will open the bath up a bit. IF you absolutely cannot do white walls (which I totally understand) then pick a light neutral gray. In the picture the floor looks a bit dark, so the white is important to open it up a bit. Cute bath. If you want some color you could paint the outside of the tub a smashing bright fun color. :D

I would keep the wainscotting white and paint with SW Window Pane 6210 ... it's a very, very light minty green/sometimes blue paint. Will reflect the light and open up the space.