Best lens for the Nikon d5100?

I just bought a Nikon d5100 camera. I'm looking for the best lens that can do everything that I want. I'm looking to shoot outdoor photos mostly of my daughter and family. I also want to be able to shoot in motion as my daughter is at the age where she squirms a lot and its hard to get a shot without it being blurry as. Any other info would be greatly appreciated.
Added (1). Some good answers I've already pretty much learned eveything about the camera, I mean all the special effects and stuff my only real concern is her moving a lot I try to take shots and they turn out blurry because of her moving last minute… Do I just need to adjust the shutter time?

Just stick with the 18-55mm kit lens you will get with it for now. This has a reasonable focal length range for most things. Until you reach the limitations of this lens, it is pointless buying more.
Learn how to use your new camera properly - read the manual & learn about photographic exposure & lighting. If you just use it in Auto modes all the time, you might as well have bought a point & shoot, as you will not get the best out of it.

There are a couple of ways to freeze motion and eliminate blur. The first is to increase to ISO speed of your camera up to 800 or 1200 ISO. This will increase your shutter speed. You will still have noise-free images at those speeds with the D5100. The second is to use a wider aperture as you shoot which increases shutter speed. Thirdly, be aware of the light you are shooting in. If you are shooting in low light, you may have some motion blur because of that.

Congratulations on your new camera.
First, learn to use the camera and lens that came with it. Outdoors, the 18-55mm lens that came with your camera is more than sufficient. If you find yourself doing more indoor photography then instead of another lens invest in a good off-camera flash like the Nikon SB-700 AF Speedlight. This flash has a tilt/swivel head which allows you to use bounce flash. Bouncing the light off the ceiling is much more flattering than using the direct flash of the pop-up unit on your D5100.
http://daniel-simon.suite101.com/use-bounced-flash-for-better-photos-a175815
http://daniel-simon.suite101.com/off-camera-flash-techniques-for-better-photos-a170120
In my opinion too many beginner photographers believe that its necessary to buy additional lenses when an off-camera flash unit would actually do more to improve their photography - especially indoors.
Outdoors on a sunny day you can use ISO 100 and your 18-55mm f3.5-5.6 zoom for about 90% or more of the pictures you want of your daughter. You've probably noticed that all the entry-level DSLR cameras whether from Sony or Pentax or Canon or Nikon come with an 18-55mm zoom lens. That's because manufacturers know that that focal length range will be sufficient for 90% or so of what beginners shoot. Sure, all manufacturers hope you'll get really hooked on photography and buy additional lenses but not everyone falls into that category. Nikon will be just as happy when you buy the SB-700 AF Speedlight.
Later, as your daughter grows and perhaps begins playing sports - soccer, lacrosse, basketball, gymnastics, etc. - then you'll likely need to upgrade your lens selection to better capture her from greater distances. The Nikon AF-S 70-200mm f2.8G might be the one you'll need.
So:
1) Learn to really use the camera and lens you now have.
2) Resist the temptation to add another lens to your kit until you know that you've reached the limits of an 18-55mm zoom.
3) Invest as soon as possible in the SB-700 flash unit. Then spend as much time as you need to really learn how to use the flash and camera together.
4) Read and study the Owner's Manuals for your camera and flash. Repeat as often as needed.
*** EDIT ***
If your images are suffering from motion blur then yes you need to use a faster shutter speed. As I said before, outdoors on a sunny day your 18-55mm zoom is suficient. Try shooting in Shutter Priority and set your shutter speed to 1/250 sec. On a sunny day using ISO 100 your camera will select an aperture that will give a good exposure and sufficient depth of field.

Best lens: nikon's 24-70 f2.8
Best solution in your case: A beginner's workshop