Verified answer

Here is a list of Nikon lens that can give you what you're looking for (close up shot with blurry background), some are pricey though. I didn't mention the 35mm & the 50mm because for close up shot you'll need to be very close of the subject with those two, especially the 35mm (and this one has a bit of distortion), if you're looking for more room between you and your subject have a look at those:

85mm 1.8 (AF won't work with your DSLR, only manuel focus)

http://www.bhphotovideo.com/c/product/84151-USA/Ni...

85mm 1.4

http://www.nikonusa.com/Nikon-Products/Product/Cam...

105mm 2.8 macro

http://www.nikonusa.com/Nikon-Products/Product/Cam...

70-200mm 2.8vr

http://www.nikonusa.com/Nikon-Products/Product/Cam...

80-200mm 2.8 (AF won't work with your DSLR, only manuel focus)

http://www.bhphotovideo.com/c/product/124669-GREY/...

I have that very camera with that very lens. I have had satisfying results with the kit lens.

You can put your camera it in aperture priority mode (A) and set to it's lowest setting which is F3.5-5.6 depending on how far you are zoomed in or out. The back grounds will be blurred nicely. At F16 or higher your entire photo will be in sharp focus.

If you want to go that bit further it is better to invest in lens with a faster aperture which has a lower F number. You can get telephoto (zoom lens) and most 70-200mm have aperture's of F2.8, these lenses though are heavy on your wallet. A much easier option is it go for a prime lens. These lenses have a fixed focal length and cannot zoom in or out. They are light and small and have low F numbers.

The cheap options tend to be 35 and 50mm.

35mm F1.8 is most definitely under £200

The 35mm F1.4 is way out if budget at over £1K

50mm F1.8/ F1.4

I would say the 50mm F1.8 is the one to get because It is a tad sharper than the F1.4 but of course the F1.4 can go that bit further in background bokeh.

It's tour choice what you want to do but I would say your kit lens is all you need.

The ideal lens for what you want is the new Nikon 50mm f/1.8 AF-G. It will autofocus on your D3100, and has the fast aperture (1.8) that gives you the bokeh you asked for.

http://www.kenrockwell.com/nikon/50mm-f18-g.htm

As for other lenses, the 55-200mm AF-S VR is an excellent 2nd lens, as it will give you up to a 200mm closer view of your subject.

http://www.kenrockwell.com/nikon/55-200mm-vr.htm

Here's a list of all the lenses that autofocus on your D3100.

http://en.wikipedia.org/wiki/List_of_Nikon_F-mount...

And here's a lens simulator, that will let you see what different focal lengths look like, through the viewfinder.

http://imaging.nikon.com/lineup/lens/simulator/

Hope this helps.

Why not save some money, and just use the Aperture Priority mode on the camera? Set an aperture that will give you a small field of focus. The larger the f number (i.e. f/22), the larger the field of focus ... the smaller the f number (i.e. f/5), the smaller the field of focus. Then, when you focus on your subject, the area in front of, and behind, your subject will be defocused. Same effect with no expensive lens purchase.

If your budget is limited, try Nikon 50mm F1.8G (around $220).