To assist you in selecting and cutting out the character or object, we try to pick a complementary color (across the color wheel) for the background. Thus, a character whose overall hair and clothes end up in the orange (includes browns) through yellow colors will get a background in the blue through violet colors. Sometimes it’s difficult to pick a background color because the 3D modeling world uses vibrant patterns and colors for their costumes—which is why we work hard to control the entire set of models (i.e., character + clothes + weapons) to a limited color palette (gamut). If we have difficulties after limiting the colors, we’ll give priority to differentiating the character’s face, hair, and torso, before we worry about differentiating background for the lower half of the character.
We’ll also increase or lighten the saturation of the background, depending upon 3D rendered product. For example, a white unicorn or a character with white hair or white clothes will get a much more saturated background than a character all clothed in black.
For more on why artists should limit their color selections, we highly recommend Color and Light: A Guide for the Realist Painter, by James Gurney (Andrews McMeel Publishing).