What would be the next best lense after a 18-55mm?

Right now I have a Nikon D3100 which comes with a 18-55mm lense. I'm looking to buy another lense, but I'm not sure if I should get the 55-200mm or the 70-300mm. I'll be using it for sports sometimes, and just things I couldn't reach before with the 18-55m. Anyone have any experience as to which one they like better and why? I'd like to keep it under $200 also. I've found a couple on amazon.com.

I went for the 55-200mm VR lens. After 200mm there can be a problem with hand holding a lens.

It won't be $200, not for anything decent anyway.

Think of it this way. Every time you change lenses you are opening your camera to dust which can get on the sensor. That's why so many of us use what's called a "single lens solution". That means you buy a lens that's both wide and has pretty good zoom as in the 18-200. That way you shouldn't have to change lenses very often. Something to think about.

The AF-S 70-300 mm VR lens costs $590 so is out of your budget. That leaves the 55-200 mm VR lens, $250.

The lower priced Nikkor lenses are fine but not up to the caliber of the two listed.

It is usually a better idea to buy a certain lens one time. If you have to save your pennies a little longer, then do that.