Nikon "landscape" lens for beginner on budget

I'm looking to start out buying a Nikon D5100 and 35 mm f/1.8 as my main walk around lens.

Was thinking about getting an additional lens for occasional landscapes when I want a wider field of view. Not sure how accurate this website is (see link below), but the kit lens (Nikon 18-55 mm f/3.5-5.6 VR lens) looks pretty sharp at 18 mm f/8, which seems to be a good f-stop for landscape based on my reading....... And it would only be 100 USD if I buy it with the camera now. If I wait and buy it later, will cost me 200 USD. Not sure I would use the kit lens at higher focal lengths much, since the 35 f/1.8 seems to beat it at the higher focal lengths.

Alternatively, I could save some money and get the Sigma 10-20 mm for an extra 350 USD, which I've heard good things about. Is there another wide angle lens in this range (10-20 mm) that is cheaper than that? I don't want to spend 800 USD for the Nikon 10-24 mm f/3.5-4.5. Any other alternatives or suggestions?? Thanks very much for your time.

http://www.the-digital-picture.com/Reviews/ISO-12233-Sample-Crops.aspx?Lens=662&Camera=614&Sample=0&FLI=0&API=3&LensComp=712&CameraComp=474&SampleComp=0&FLIComp=3&APIComp=3