Sigma 18mm-125mm or Sigma 18mm-200mm for a Nikon D5100

I'm a learning photographer ready to take the next step and buy my first DSLR! So after quite a bit of research (and trying to keep within my budget) I have decided on the Nikon D5100. Now I'm trying to decide which lens to get to compliment my camera nicely.

The reason I'm looking into getting a zoom lens such as the Sigma 18-125 or Sigma 18-200 is because I'm going on a backpacking trip to Europe for two months and definitely don't want to carry much more gear around while also running the risk of getting dust on the sensor and lens. I understand the obvious difference in zoom range, and am okay with either one. I want to get the lens that will be of the best build/function and, of course, will produce the best images. So after looking for info on both Sigma lenses, I'm just going to ask you strangers for your opinions and advice. Hopefully some of you know enough about lenses or at least where I can find a useful comparison to look at.

The 18-200 mm will give you the most range, but of course you know that I'm sure.

You pay a price in image quality for having more zoom range, and with many (not all) Sigma lens you pay a price in image quality for it not being the Nikon brand. Those seem to be true of the lenses you're considering. If you can afford the Nikon 18-200mm AF-S VR II it should give you better quality than either of the Sigmas with great versatility. The Nikon 18-105mm AF-S VR is less expensive, and it sacrifices a lot of versatility, but it should give the best sharpness through its range.