I have a D800 and just yesterday completed the repairs on my 14-24 lens, which I got in broken condition and repaired it myself. Zoom is a bit rough but decent, autofocus is perfect, image quality and sharpness are top notch.
I think that the 14-24 really fits my personal preference for a daily use lens more than any other. I have found that I LIKE wide angle shots, at least, when you have pixels to spare.
It's the only one of the trinity that I own yet.
My "general purpose" lens is an AF-S 24-85mm F/3.5-4.5 G ED. This would be, for most people, the most use lens for walking around, being almost exactly the FX equivalent of the common but very good DX 18-55mm lens that is the kit lens offered with virtually every Nikon DX format camera in the last decade. This is definitely a versatile and affordable lens that I think should be in your bag.
The 24-120mm F/4 lens is well regarded but I have no personal experience with it. I'd get one if the price was right.
My long distance needs are covered by a Tamron 150-600mm "tamzooka" which I have been very impressed with. It's very sharp and it autofocuses very fast. It is my go-to lens for photographing racing events and other fast moving action. It is well worth checking out.
My next lens will be, I think, the 24-70mm F/2.8. It has to be popular for a very good reason.
I'd say that the trinity is probably the right answer for most photographers, plus a portrait lens of your choice and a super zoom if you're into birding, wildlife photography, or photographing racing events.