Nikkor 55-300 mm or 55-200mm?

55-300mm is creepy on
focusing, 70-300mm is bit over
my budget.55-200mm seems
better with half the price.any
other 3rd party with AF in
55-200or300 range.
Appreciate recommendations
and suggestions for my D5100
body. Will that extra 100mm
matter for my first telephoto
lens.

Depends on why you want a telephoto lens. If you want to birding or wildlife you need every mm you can afford.

Due to the effect of the inverse square law, the difference between the 200mm and 300mm is not significant. It's a 1.5x difference. It is noticeable, but not a real significant change.

To get an idea, try this lens simulator by Nikon. It will show you what the different focal lengths will look like.

http://imaging.nikon.com/.../index.htm

Be aware that Nikon makes two different 55-200mm AF-S lenses; one with Vibration Reduction and the other without. VR is nice to have for a beginner, and when you compare the 55-200 VR version to the 55-300 (which has VR) there's not a significant cost difference.