An important function of the background in portraiture is to blend or contrast with the foreground.
This depends on the pose—a well-lit profile against a dark background works well, while hair highlights dropping into a white area can create an airy feel. A vague halo of shading added to a portrait is seldom successful. If you don't want to attempt a background, leave the background a crisp white. However, if your source photo is lit with a front flash, this can make it difficult to model the form, as the white highlights are in the foreground and the white paper tends to sit on the same visual plane. Most portraitists favor a background of middle to dark value because it enables them to use shading and softened detail to model the form of the figure. A more complex background, whether outdoors or inside, can work well, but keep it as simple as possible when you start out.
Whichever approach you favor, the background deserves as much attention as any other part of the drawing. There is no point in pouring hours of tender loving care into the rest of your portrait, only to do a vague scribbled background. The energy in briskly applied marks actually draws the eye away from more detailed areas of the drawing, too, making the contrast doubly apparent.
