A standard zoom for D800?

I would not listen too much to the reviewers. They always dislike lenses which are not the fastest and the most expensive. I have the 24-120 and I am very happy with it. It covers the range I need from such lens and I am not bothered by the f/4. It is a weather sealed well build lens, sharp enough all the way, so what more would you want? Of course, it is not f/2.8 but so what? I am pretty sure even the 24-84 is OK if you can live with the variable aperture and the less range. Don't listen too much to those reviewers, visit a well assorted shop, ask them and I am pretty sure you can test the lens on a D800, take a few images and take them home with you, check them out at home and buy the lens which you like most. They are all fine if you know how to handle them and what to do with them. Most people shoot f/5.6 or even less with those fine zooms anyway, so don't bother about that.

Get a couple of fine primes for the money you save and you are better off with those when fast lenses are needed.

Just one more thing... also the 24-120 is quite big and not very light, but that's the price you have to pay if you want that range on an FX with constant f/4 aperture. Have a look at third party alternatives as well. There might be something you like even more than the Nikons.