Depends...since the vanity is small, I'd tile under it. The wainscoating, I'd probably omit. Depends on if when you remodel the next time, you still like the floor tile and wainscoating. I'd consider carrying the wainscoating past the point where the vanity butts up against it, as cutting the tile so it looks good would probably be harder than just placing the vanity up against that strip of tile. You can always shim between the back of the vanity and the wall to compensate for the thickness of the tile. If you are using wall tile, rather than a hard floor tile on the wall, it is fairly easy to drill a hole in, so I wouldn't worry about that. My unprofessional opinion.