Please take everything I say below with a grain of salt, I am not the great expert, I am just a hobbyist. I'm just giving my opinion.
That said, IMHO all these zooms are good, the 14-24 and the 70-200 I think can even safely be called 'great'. I think in the 14-24 range, since the great primes are also very expensive, this zoom is even good value for the money. I don't have it, but I'd like to have it

because I've seen its IQ and am impressed.
In the ~ 24-70 range, I personally use primes. I have both the Nikon 50mm f1.8D and the Nikon 50mm f1.8G. The G is generally sharper across a larger portion of the image, the D seems more pointed, and requires you to use the optimal settings to deliver best results. As for the other relevant IQ aspects, both lenses are very good. The G is IMHO easier to use, as it is equally good pretty much everywhere and at all settings, so you don't need to 'know' the lens so well to get optimal results.
I also use the Sigma 35mm f1.4 DG HSM. The IQ of this lens is stunning, and its sharpness makes it an ideal companion for the D800. I am very impressed with the image and build quality of this lens, and it is a lot cheaper than a comparable Nikon lens (and that Nikon lens is also not free of problems), and delivers IMHO almost unrivalled image quality. And with the Sigma USB dock you can adjust the focussing in great detail. But it has a few whims I first had to come to terms with.
First, that USB dock gives you three sliders for adjusting the range between 0 and approx. 4 ft. And then one more for all the rest. That seems unbalanced, especially as, as I will describe below, the lens would benefit from an additional slider for the range between 4ft and infinite.
Because (and this is the whim I mentioned above), if I set the lens up to focus perfectly at everything up to 2 or 3 meters, I get a quite pronounced backfocus at around 6 meters (version a). If I allow the lens to have a front focus of a few centimeters at 1.30 meters, everything beyond 2 or 3 meters is perfectly fine (version b). I have used the lens for a few weeks now using version b settings, and I have to say that in everyday use, none of this has so far become apparent. I only noticed it in test sessions. Also, I have been told that the D800 may show these issues more clearly than cameras with a lower resolution, and indeed, in images downsized to screen resolution, these issues are not as visible as at full resolution.
However, it seems that quite a few copies of this lens have focussing issues. The lens I described above is the second copy I have, the first one had the same symptoms, but more pronounced. This second copy creates perfect images in everyday use, the issues are not a problem when shooting on location, but if you buy this lens, you should maybe buy it in a shop where you can try two or three copies, or you should be prepared to send it back if you mailorder, and order a second copy, until you get a good copy.
A lot of people also say their first copy worked, I don't want to doubt that, maybe I just had bad luck. But there are others on Amazon who report of having had a bad copy, or even two, so I am apparently not the only one seeing these issues.
I also use the Nikon 85mm f1.8 G. It also offers excellent IQ across the entire image area, and at a very moderate price.
Regarding the 24-70 zoom, I've seen test images taken with this zoom compared to the highly acclaimed Tamron 24-70, which if you believe DXOmark is the sharpness king of all zooms. But those test images show that the trusty old Nikon AAMOF is sharp even up into the borders and corners, so in most of the image area, it is actually sharper than the Tamron, even if the Tamron beats it in the center in terms of sharpness.
It seems that this Nikon 24-70 can have issues with CAs. But there are also users who say it hasn't, so maybe a good shop where you can chose between different copies is again recommendable?