AF-C is usually employed where the subject is in motion. Sports is a good example of where I use AF-C. I prefer the "Release + focus" option when using AF-C. For relatively static people subjects like those you mention AF-S would normally be used rather than AF-C.
With moving subjects like in sports Dynamic is commonly used in conjunction with AF-C with the number of points chosen on the basis of subject movement. I use 9 points.
Some of these settings you will choose on the basis of your experience. There's frequently a trial and eror period involved in determining what settings work best for each individual. Not everybody uses the same AF system settings for a given task.
This is to add some specificity to my previous comments. If I were shooting the people subjects you mentioned I would choose AF-S (Single-servo AF) via the focus-mode selector on the front of the D700 and Single-point AF via the AF-area mode selector on the back of the camera.
I presume that you moved to the D700 from a simpler camera and are finding it a whole lot more complex to deal with. In a short time much of the complexity will lift, and you will be rejoicing in what a great selection you made in purchasing the D700. I consider the D700 to be the best bang for the buck in the whole Nikon camera lineup.