Should I purchase the Nikon 55-200mm VR lens?

I recently purchased the Nikon d3200 with the 18-55mm kit lens. I'm now looking into getting another lens. For action shots (sports) and portraits, would the 55-200mm VR lens be a good choice, or is there another one that is better? Also, for shooting video would it be a good choice? I have done lots of research on DSLRs but there's still a lot about lenses to know.

The best sports/action lens is the 70-200mm f/2.8, as it allows you to use a faster shutter speed in most lighting situations. However, the 55-200mm f/4~5.6 should allow you to take OK sports/action photos in good daylight conditions.

I bought this lens for my son, and I have found it has some blurry areas when used wide open at f/5.6, and even at f/8. This all clears up by f/11, so you may not find it is the sharpest lens when using it for sports/action photography at wide open apertures.

Here are some sample photos of this lens, showing the blur in the most extreme areas of the lens.

http://www.althephoto.com/lenses/con-telephoto.php

If you can limit this lens to 150mm (and not zoomed in to 200mm), you will get much sharper photos.

But still, he uses it at hockey games, however he has to really crank the ISO up to get a decent blur-free photo.

In contrast, the 70-200mm f/2.8 will let in up to 4 times more light (over the 55-200mm f/4~5.6 at it's wide open blurriest aperture), which is why it is superior for action photography.