AF-S DX NIKKOR 55-300mm, AF-S DX VR Zoom-Nikkor 55-200mm or AF-S DX Zoom 55-200mm?

I'm getting a new lens for my Nikon d3100 and i need a lens that can zoom quite far and won't really cost me a lot

Added (1). I personally prefer the AF-S DX NIKKOR 55-300mm since it can really zoom very far and btw the 18-55mm lens if does not have any gaps

Af-s dx vr zoom-nikkor for sure, i have it and love it. I tried all three actually in a store and saw a total difference between them. The one i mentioned is the best

The difference between 200mm and 300mm is quite substantial… Whether it's enough of a difference to you is difficult to judge. Between the two 200mm lenses, get the VR one, price difference is minimal and VR is nice to have on a long lens

Long zoom? Tamron 18-270mm 15X zoom lens. Of course that would have a slightly smaller magnification power than the 55-300mm 5.45X zoom lens from Nikon. Clear up your mind. Stop thinking about zoom. You are correct though when assuming that 300mm goes longer than 200mm but you are using zoom in the wrong sense. Heck a 1000mm non-zooming lens will beat all of these lenses when it comes to pulling far objects close to you. My point is, get your terms right and when you already have a decision, go for it.

Gaps? If you are really after getting very far closeups and you already have the 18-55mm kit lens, you can get the 1000mm non-zooming lens and to hell with the 56-999mm gap. You might want to read this.