What are some good lenses with big aperture for a D3100?

So a i just buy this camera (Nikon D3100) and these lenses SIGMA 18-200 f/1:3, 5 - 1:6, 3, and i find myself complaining about the small max aperture of the camera, that really make it hard for shooting photos in low light, and don't give such a high dof, and i was thinking about buying some lens with a bigger max aperture, it may be with a fixed focal length(i think a 18-55 would be more expensive, i don't really know much about price tags), but anything lower than 35mm, i tried searching for models, but i'm not sure when the models are compatible with my camera, i would really be thankful for any help

Look for some on this link for lenses that are f/2.8 or faster

ALL AF-S lenses will work with your D3100

http://www.nikonusa.com/...index.page

The smaller the f/number, the larger the aperture.

http://www.bhphotovideo.com/...4294185277

For budget lenses with large apertures and built-in autofocus motors, you can look at the Nikon 35mm f/1.8 af-s, 50mm f/1.8 af-s.
http://www.kenrockwell.com/...mm-f18.htm
http://www.kenrockwell.com/...-f18-g.htm

There's also a 50mm f/1.4 af-s, but it's relatively expensive.
http://www.kenrockwell.com/...14-afs.htm

Nikon's also just released a new 40mm micro (macro) f/2.8 af-s lens that looks promising for your D3100.
http://kenrockwell.com/...mm-f28.htm

For zooms, Nikon has excellent fast lenses, but they can cost quite a bit more. The 70-200mm f/2.8 is a gem, but will set you back over $2, 000.
http://www.kenrockwell.com/...0mm-ii.htm

I'd seriously consider some quality 3rd party lenses here. Personally, I shoot with a Tamron 17-50mm f/2.8 and a Sigma 70-200mm f/2.8. For their price, they give pretty good performance. The big plus is that they'll autofocus with your D3100.
http://www.the-digital-picture.com/Reviews/Tamron-17-50mm-f-2.8-XR-Di-II-Lens-Review.aspx
http://www.dpreview.com/...0_2p8_n15/

As for your last question, here's a link to a regularly updated list of lenses that will autofocus with Nikon's entry level DSLR's.
http://en.wikipedia.org/...cus_motors

I think the 35mm prime would be a great starting point for you.