Ok I admit I haven't made a clear choice on what lenses to buy.
Well, as a general set of lenses with excellent image quality, I can recomment the AF-S 16-35mm f4 VR and AF-S 70-200mm f4 VR duo which I use, and for which at the moment there still is no better option available.
The AF-S 16-35mm f4 VR isnt outright brilliant, but IMHO the best all-around package of all available options. If you think you dont need 16mm (to me thats the highest focal length I personally still would accept as lowest border, but depending upon your taste you might not need it) theres a AF-S 18-35mm (not sure about f-stops, I think f/3.5-4.5 ?) thats cheaper, smaller, more lightweight and optically at least as good (but dont expect wonders from either of them - if you really want sharpness in wide angle on Nikon F, theres no way around the heavy bulky AF-S 14-24mm or the brand new heavy and bulky Tamron 15-30mm f2.8 VC, or those Zeiss manual prime lenses. With the zooms I specified, try to shoot them at f/5.6 for optimal sharpness, avoid the extreme ends of the focal range, and dont have too high demands for border sharpness either. With those cheavats, I typically use my 16-35mm as a 21-28mm f5.6 and cant complain about the results, especially since I rarely do landscape. And yes, sometimes 16mm is not wide enough, but there you go, cant have everything).
The AF-S 70-200mm f4 is simply excellent. But if its too pricey for your taste, the good old AF-S 70-300mm f4.5-5.6 VR is no slouch at all either. If you think you want more light, the AF-S 70-200mm f2.8 VR2 is of course brilliant too. Theres also cheaper options for f2.8, like the old AF-S 80-200mm f2.8; you might want to think about getting a monopod for using this too, because it has no image stabilization.
Add to those two zooms (or whatever variant specified you choose) an AF-S 50mm f1.8 (or AF-S 50mm f1.4, or Sigma 35mm f1.4 "Art") as a lens for low light and a Tamron 90mm f2.8 VC macro (or AF-S 105mm f2.8 VR micro) as a macro lens, and that would be a great general setup for "anything".
I personally hate "normal" zooms. I think in that focal range, prime lenses are simply vastly superior, and the only reason not to use a prime lens is if you're too lazy for zooming by feet. But others have already made pretty good suggestions about this type of lens, so fortunately I can skip that anyway.