I need a speedlight for Nikon D3100?

Could you please suggest me a good speedlight for my nikon D3100 not too expensive.
And also a filter. What kind of filter do i need (polarizer, neutral density etc).
I'm just a beginner and i would really appreciate your advises

The least expensive flash is the Nikon SB400, but unless you intend to shoot a lot of events, the on-board flash will do the job

http://www.kenrockwell.com/.../sb400.htm

The filters you need really depend upon your and what you tend to shoot

* You need a UV or NC filter to protect your lens(es) from sticky fingers, mud, etc.
* You only need an and filter if you expect to shoot moving water and make it look like cotton. For that you will need a 10 - stop and filter. If you are shooting landscapes with bright a bright sky, you will need a graduated and filter
* Polarizing filters can be used to darken the northern or southern sky (this works best when the camera is aimed 90 degree to the suns arc. It can also reduce reflections off glass or water.