Ai = Automatic Indexing; i.e. the lens tells the camera what aperture is in place without using additional linkage or action. Came about because Nikon had kept compatibility for a long time with old camera body and lenses. Very old non-Ai lenses mounted on a non-Ai camera needs to go through a procedure to first hook the lens "rabbit ears" with a mechanical link on the camera, then turn the lens aperture to the minimum then back to the maximum to "index" the lens. Very leche.
About the oldest lens you should mount on your D600 are the Ai. Identified by the rabbit ears with holes and secondary aperture reading on the aperture ring.
Ai-mod are older non-Ai lenses that are modified to Ai spec for use on "modern" cameras. You can use Ai-mod lenses as well.
AiS lenses are immediately before AF and some are still available new today.
All the above are manual focus lenses. Some of us (Ben is one) have loads of manual focus lenses. Indeed I use MF more than AF.
MF lenses are like swiss watches, precision made, beautiful to hold and turn, slow to use as the are MF. More durable than AF lenses. Some are as good if not better than AF counter parts. The AF 28mm f/2.8 is one such lens that is way way way inferior to the MF counterpart. Most AF lenses are like Casio watches, functional and great features.