Zoom lens for Nikon camera? - 1

Hi, i'm looking to buy a new lens for my Nikon D3100. I'm looking for a lens that will allow me to zoom in further than the standard 18-55mm kit lens. I need a lens with a motor built in (AF-S), and I want it to have Vibration Reduction (VR, or whatever the other brands call it). Want to spend as little as possible, as this is my first DSLR, and i'm not using it for professional purposes. I originally considered the AF-S VR 55-200mm Nikon Nikkor lens, but now I'm considering the 55-300mm version from Nikon. I've also considered getting a Tamron or Sigma, I just don't know what to be looking for when it comes to AF-S and VR. Can someone point me in the right direction in what to get, and where the absolute cheapest place to buy it would be. I'm in the UK and would ideally like prices in £GBP. Thanks!

Added (1). I never said I 'need' Vibration Reduction, I said I want it.

1) Don't bother with Tamron or Sigma lenses. 2) Just get the 55-200 VR… They only cost about $150USD and are reasonably sharp. 3) Why do you NEED VR? Amazon usually has good prices.

Hi
if cost is the issue then the tamron or sigma are the answer.
now we come to the real question AF-S auto focus this must cost more so it will be a premium one.
then we have the VR or vibration resistance which is like a non shake system yet again it comes down to cost again.
now a good tripod will pay dividends when it comes to reducing shake and vibrations.
so if you use a tripod it will help with long telephoto lenses as shake you will even the best say that.
like you i have a nikon and mine is the earlier version so it has similar problems, in may case it is age which is the issue and a bit of shake is common in older people.
yes the best one is the macro Lens which can also be used for close up work as well a distance.