There are also some other types of old Nikon lenses.
Nikon F mount Pre-Ai - these lens will not mount any of the modern Nikon cameras.
Nikon F mount Ai'd (or Ai'ed or Ai converted) - These are Nikon F mount pre-ai lenses that were converted to Ai. Most were done by Nikon because Nikon offered to convert them for free at all NSC in the past (these were called factory Ai'd). Those not done by Nikon are quite rough, since the conversion involves sawing part of the flange off the mount, though I have seen some that we done very smoothly also.
Nikon Series E - These are basically same as Ai lenses but cheaper. Not as solidly built as Ai/Ais lenses, some are even mostly plastic. They still work just like Ai/Ais lenses though.
Nikon AF - these lenses are autofocus lenses that use the screwdrive motor in the camera body to attain Autofocus.
Nikon AF-D - Same as Nikon AF, just that the D denotes that a new chip is added into the lens so as to send Distance information back to the camera. This "D" is important, especially for TTL flashes.
All lenses without the "G" designation will have an aperture ring. Any lens with a "G" designation do not come with aperture ring, and aperture can only be controlled via a compatible camera body. And yes, there were a few AFS lenses which are non-G with aperture ring, one of which is the
80-200/2.8 AF-S.
For compatibility, this is a good reference with a chart for you to refer to:
http://www.kenrockwell.com/nikon/compatibility-lens.htm