New Nikon Camera Lens?

I have a Nikon D3100 and I wanted to buy a new lens under $250. I want to be able to use it for close up action shots and for pictures of the moon. I was thinking about this one lens that has good zoom but most of the sports pictures turned of blurry.

I use a Sigma 80-300 dg zoom, under a hundred quid its fantastic.

how?
Use a tripod

Select manual focus mode.put it into live view, press the + button and the image will zoom in, you can focus manually to get the sharpest image.

Put your camera on M, set the aperture to f8 and shoot at a variety of speeds from 1/250 to 1/1000th.

you will have to move your camera as the moon moves at quite a speed

Well, first I would stay away form other brand lenses.
You are just going to run into compatibly problems ETC.
Stick with the good old Nikon.
Your kit lens (18-55mm lens) will have pretty good macro.
If you are a serious macro shooter get the Nikon 40mm lens.
For action shots you could use a Nikon 55-200mm lens with out a problem.
You just need to know how to shoot fast moving subjects.
You really can't find a lens with great macro and a long focal length.
You can't get the lens your are looking for, for $250.
I would get the 40mm lens for macro.
After awhile you could get the Nikon 55-200mm lens.
I had that lens before I went to FX and got some really good blurr free action photos.
Just learn your camera (And take it out of AUTO mode) and you will be fine.
Have fun!