For the main mounts (Nikon, Canon, Sony, Sigma, 4/3rds) the "3rd party lens makers" (Sigma, Tamron, Tokina) make lenses that fit and provide AF and other functionality provided you buy a lens that built for your camera. No Adapter needed.
In your first post it sounds like you have older lenses that you may want to use that are not Nikon?
All Nikon from the last 50 years lenses will mount. How they work, depends on your camera. If they are not Nikon and you are thinking of using an adapter, simply stated - forget it and go buy a new lens. :)
One exception: If you have great Leica or Zeiss glass, or are attaching Cine lenses for video, then spend the money for a good adapter.
Real good adapters from Novoflex run around $250 give or take the given mount. These are probably the best engineered pieces that are tested and matched to a lens and body for optimal usage. There are others that range from $15 to $200 and work ok, but have various drawbacks (like the lens will not close focus or focus to infinity, etc).
Generally unless you are just playing, or trying for a particular "look" like an old Diana or Lomo lens, I would stay away from them.
The problem with adapters is that they are like toys from a Crackerjack's box - you never know what you will get. I have used great $20 ones and really bad $150 ones. There is really no way to know until you try them or do allot of research.