AlanF's posts make the most sense to me. I've tried the 500 f/4 series 1, as I have said elsewhere...and the copy I tried, was very soft, and also didn't focus accurately or consistently. It was tested and supposedly nothing was wrong. After this, it seems to me the series 2 are the only choice, if you want a big white lens.
I would suggest the 300 and 600 series 2, plus both series 3 extenders...unless you don't ever want to shoot birds. This combination gives you 300mm, 420mm, 560mm, 600mm, 840mm, and 1200mm.
For much closer subjects, especially in low light, I would say buy the 200 f/2 and forget the 70-200 f/2.8 series 2. The 200 f/2 has better color than perhaps any other lens in existence, despite those on here who think it's "not such a special lens". I'm sorry, but yes it is. I don't own one at this time.
If you find that you prefer to shoot in low light, but your subjects are kind of distant, then the 400 f/2.8 is the obvious choice. Say, a person at 100 to 300 feet away. I have craved this lens, but I think for me the 300 f/2.8 makes more sense. The FOV at 400mm is going to be too narrow a whole lot of the time, for me.
The 500 f/4 series 2 is best for birding (combined with the 1.4x iii as needed), especially if you need to carry it a long way (lighter and smaller than the 600, and not much less reach).
If you would really like a zoom, wait for the 200-400 f/4, probably released this summer. It seems to me, it would be incredibly handy...and cost less than buying two or more other lenses covering the focal range from 200 to 560mm. Of course, it's far from being as low-light-capable, as an f/2.8 lens...especially with its TC switched in.
As for autofocus, I personally opted for the 6D rather than the 5D3. I have found it doesn't take much tweaking to get very nice servo AF via the 6D. The thread that stated the 6D wasn't responsive while focusing, is just wrong. I realize the 5D3 choirboys will hate on this, but I'm just stating my experience. And yes, I've tried the 5D3. The 6D seems to excel at servo tracking in light requiring ISO 25,600 on an f/4 lens (with center point selected), and absolutely nails it a high percentage of the time (perhaps 70%). But this climbs to near 100% if you set the servo for accuracy rather than speed for "second shot"...of course this slows the fps...which is fine with me in these situations. I would rather have all the shots in focus and not waste time and memory on blurred ones. So in these situations, slowing the fps by 20 to 30%, doesn't seem like much of a loss. And this is using a much-maligned series ii, 2x TC (I got it free and don't mind using it at all, on certain lenses. It does hamper contrast and color, but leaves plenty of sharpness intact...on the right lens. On the wrong lens, it's not quite acceptable, at best).
I of course admit, in decent light, the 5D3 is the one to have. Or the 1DX for any situation, if you don't mind it's mass and cost.
I also agree, that the new full frame cameras have increased their resolution more so than it seems they should have. I don't know if this is due in equal parts to the sensors themselves and to the processing...or if it's one more than the other. Either way...I'm astounded at how much I no longer need a crop sensor for "reach". (And please no chiding about how I'm "not the first to notice this"...I know I'm not!).