Advice me for a zoom Nikon FX lens?

I want to buy a zoom lens for Nikon D5100 [now have only the kit lens 18-55mm].
I've selected this options

AF Zoom-NIKK0R 70-300mm f/4-5.6G
Tamron AF 70-300mm F/4-5.6 Di LD Macro
Sigma 70-300mm F/4-5.6 DG Macro

Which will be cool? Will there be any visible optical difference in the images?

First consider the weight of the lens. I a professional of many years made this mistake last year! I bought the Tamron 28-200mm and found that besides the lacking of quality (not as sharp as I required) that the lens was just too heavy to carry around attached to the camera for more than a half hour! So bite the bullet and get the Nikkor lens. Personally the 300mm is still too long for me, I prefer the 200mm (50mm-to-200mm) on my camera.

The AF Nikon zoom 70-300mm will not autofocus on your camera as it requires an advanced Nikon camera with an autofocus motor built-in to the camera. You need the more expensive AF-S version as this one has an in-lens focus motor.

I'm not sure about the other two lenses, but make sure they also have in-lens focus motors - not all do.

Many people that own entry-level Nikon cameras prefer the AF-S 55-200mm or AF-S 55-300mm lenses, but they are DX lenses. Unless you are looking specifically for a FX lens, consider the DX lenses as they will autofocus on your camera.

Those cheap 70-300mm lenses will have inferior sharpness, especially close to 300mm. The Nikon 55-300mm AF-S VR DX would be better. The expensive Nikon 70-300mm AF-S VR even better.
These telephotos make the camera kind of front heavy. To get good results you need a tripod, and not a cheap one. A 3-way panhead is best, and a pretty substantial one like this tripod
http://www.bhphotovideo.com/...ripod.html
or a head like this one to put on your legset
http://www.bhphotovideo.com/..._Head.html