Paint the walls, yes. A soft white like SW Alabaster. The vanity is fine. It adds a much needed note of natural material to the room. Then replace the lighting.

Paint, new vanity lights, change knobs and possibly other hardware. The photo won’t enlarge for me, and I don’t know the decor styles you like, so it’s hard to be more specific. Is this is a house you’re looking at, or already yours?