You see, the trick with green screen for video is that the scene contains moving elements—if nothing else, that weatherman standing there isn't standing perfectly still. So, the producers need a fast fix for keying the subject from the background. They chose bright green as a color that's not seen in humans, and not common in our clothing, either. With a single mouse-click the bright green is keyed out and replaced in processing with a new background image.
There are challenges with working with all of this green. The biggest problem, of course, has to do with lighting that bright color. If you position your subject too close to the background, green light reflecting from the background can give your subject (or even just his or her edges) a subtle, sickly green cast. Worse, even if you do allow enough distance between subject and background, shiny surfaces like shoes, buttons and eyeglasses can still reflect that green background—and that ain't good.
In the still world, we don't need a single-click solution to masking subjects out of backgrounds. Sure, convenience is nice, but with great tools like Photoshop's Magic Wand and Quick Select tool, it's not exactly a long, time-consuming process to separate subject from background. The green isn't necessary, and for the reasons outlined above, it's risky too.
So, what color should you use in the background of an image destined to become a composite? Simple: match the color of the background to the color you're going to drop in. Neutral tones like white, gray and black will ensure that you don't reflect a color cast onto your subject, and precise color choices (say, blue if you're going to composite your subject against a blue sky, or red if the subject is destined to be dropped in front of a red brick wall) mean that any color cast you do create isn't a detriment, and can actually add to the overall look.
More than anything, though, matching the color of the background you use to the actual color of the eventual background means you'll have less trouble blending the two images seamlessly. No more glowing green halo edges, or an outline of stray white pixels. Now that subtle little color remnant, even if it's just a pixel wide, will help blend the subject with the background rather than spoil the illusion and give away that the work is a composite.