Choosing the right fixture is essential when it comes to a bathroom. The first this to keep in mind, is that you need a property amount AND type of light. Meaning, you need ambiant and task lighting in the same room. If the electrical wiring in the bathroom was done properly, you will have a junction box in the ceiling, one above the mirror, and one on either side of the vanity mirror. If it is a small bathroom, you may just have one outlet centered above the mirror. The ceiling light usually provides general or ambient type lighting. The fixture above the mirror and on either side of the mirror are there to provide task lighting. It is important to have fixtures on either side of the mirror not just as task lighitng, but also to avoid shadows while grooming.
Swing arm wall lamps are not usually meant for the bathroom, but there are a variety of make-up mirrors with extending/swiveling arms to accommodate shaving or applying makeup. This may be something you want to consider as an option.
After you have determined the placement of the fixtures, you can move on to choosing what style of fixtures you want. This can include the design, the size, the color and the material that best matches the style of your room.