Best zoom lens for Nikon D5100?

I received the Nikon D5100 for fathers day and prior to this have had no experience with DSLR's so I'm very new to this. I have been shooting so much since getting it and reading everything I can to get experienced. An 18-55 lens came with the camera but I would like to be able to zoom some more. I'm not looking to break the bank, just get some more zoom to learn my camera better, even if it means I have to buy a more expensive lens a year from now. I appreciate your help.

All the zoom lenses made by Nikkor are excellent.

If you are looking for a one lens solution, then the 18-200 mm lens should do the trick

For clarity, you really do NOT need a zoom lens to learn how to use your camera better.

Here is how you can learn to better control your camera

http://camerasim.com/camera-simulator/

The 55-200mm VR will be a much cheaper alternative.