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Today I'm using the 70-200 for everything, either with a TC or without.
I want the 300mm because of the better IQ and reach, so I don't need to use the 1.4x III, but when I do, I don't want to get hit with the IQ bat too much.
I don't do wildlife so much, so 500mm will just stay at home 90% of the time, so I prefer a TC usable lens instead of a "stay home" lens. The 500mm F/4 L IS cost almost as much as the 300mm F/2.8 L IS II (difference is about 700$ for me), so I don't want to buy both.
Next year I plan to go to africa for a few weeks, and for that I will rent a 500 or 600 if I don't feel the 300+2x is enough, but I won't buy either at present time.
Since you say the difference between the I and II is very little, I will just go with the I.
But I will look into the new 120-300 sigma. The reason I don't like the sigma as much, is because of the filter size (105mm) and the weight/size of the lens. I don't use tripods so much, so the extra weight for the long run might bother me.
I'm not a big person to say the least (1.68cm, 64kg), but I can handle the weight up to a certain point. 2 bodies, 70-200, 300, 2 extra short lens and a macro lens, carbon tripod and some stuff, I can handle so far. But there is a limit to how much I want my back to carry.
My plan for sports to use 2 bodies, 5D3+70-200 and 1D4+300.
When I do wildlife, I go with the 1D4+2x+70-200 to get a 140-400 reach (before the 1.3 crop), and I usually use it around the end of the reach, so I don't really feel I need the zoom.