Both sides of the mirror are best for casting an even light across the face, especially when grooming and applying makeup.

You might take a look at any one of several mirror cabinets with a built-in LED vertical zone of light on each side to cast the even light noted above. As to a surface-mounted fixture that is fairly clean looking, provides a soft glow of light, but has some traditional appeal, take a look at the Ginger Kubic fixture.