Nikon d3100 third party lens compatibility?

I'm thinking of getting a D3100 body and pairing it up with some kind of general purpose 18-200 or whatever… It's been a while since I've been into photography and my knowledge about these new digital camera's is somewhat limited. As far as I know the Nikon D3100 requires lenses with their own AF motors as it does not have one in the camera body. Do the third party lens makers like Sigma make them for this camera, with their own motors?

Yes, sigma, tamaron + other brands make lenses that will fit a nikon d3100 body

Yes. Sigma calls them HSM, Tamron BIM or PZD. Tokina makes no such lenses as of now as far as i know.

For a 18-200mm lens, i wouldn't consider anything else than the Nikkor one though. Yes, it's significantly more expensive, but it has the reputation of being the single best superzoom lens available for DSLRs. Pretty much all others have a mixed reputation regarding their image quality at best.It'll be worth it to save for the Nikkor.