It all depends on what you want to do. I lurk on the D7000 forum because I am a likely future D7x00 owner, but my wife and I currently shoot D90s, which are the predecessor to the D7000. I think your lens questions are independent of which DX body you are looking at.
First of all, the 35 mm f/1.8 is a no-brainer. This is a superb fast lens at a great price for DX format shooters. It provides the DX equivalent of the old "50mm lens" from film days. It's fast, sharp, and cheap. (Typically you only get the chance to choose two of those three features!)
The zoom option is where your particular interests come into play. Unless you have a real need for constant f/2.8 in the 17-50mm zoom range, there are a variety of other options you might want to consider. The Nikkor 18-200mm is a very useful lens for those seeking a single lens DX solution. My wife uses this as a primary lens on her D90, paired with a Nikkor 105mm f/2.8 macro to feed her passion for close-up nature photography. The 18-200mm lens is capable of excellent images -- the cover photo on the February 2013 issue of Outdoor Photographer, which hit my mailbox today, was taken with a Nikkor 18-200mm lens on a D300.
If you don't need constant f/2.8 or 200mm, there are a couple of additional options that will give you excellent images and save you some money and some weight around your neck. The first is the Nikkor 16-85mm VR lens. This is an excellent all-around "standard" zoom lens on DX bodies and is the lens I have on my D90 most of the time. As former amateur Nikon enthusiasts abandon the DX format in response to the siren call of Nikon's new FX bodies (D600, D800) the prices for excellent used examples of this lens have dropped a bit. Second, do not ignore the Nikkor 18-105 VR "kit" lens that was sold with lots of D90s and D7000s. It is not quite as robust in build as the 16-85 (e.g., plastic rather than metal lens mounting plate), but it produces excellent images, provides more reach at the telephoto end while sacrificing some wide angle capability, and is available VERY inexpensively on the used market as people offload the lenses they acquired when buying D90 and D7000 kits.
So, as I said at the beginning, it depends on what you want to do. There is no single right answer, but one of the many possible answers will suit your photographic needs and budget.
At the end of the day, it's more important to go out and take photographs than obsess over the equipment...