What's your budget?
I've travelled through that region a lot and had a base in Cape Town for around 18 months of that time. I've visited a number of the National Parks in SA and across the border into Botswana and Namibia.
Overall, I feel the 100-400 IS L is the best all round lens. You can hand hold and shoot which helps if you're in a group and it's hard to get a firm support anywhere and the driver keeps the engine running!! A Sigma 50-500 will also do a great job and would perhaps be first choice if I was self driving, which I usually do. Then it is useful to have a bean bag to rest the lens on the car door frame.
You will get good shots with 300mm but you will also lose plenty. Animals are at varied distances so I would advise against a prime ... personal choice. A zoom is more flexible when you're tied to a vehicle. The 300mm IS L and 400mm L are both excellent lenses tho' if you want a prime.
The 100-300mm f4 Sigma with TCon is flexible as it does well in lower light game drive conditions, but you can add the TCon when the sun gets higher. Excellent quality.
The 70-200mm will do decent portraits if you have the room to frame, but would be a waste of time, on the whole, for safari conditions. Some will have got some decent shots with it but generally the keeper ratio will go down significantly compared to the 400mm and over options.
Portrait 50mm 1.8/1.4 or 85mm 1.8 are classic choices. Depends what you mean by protrait tho'. I'd get a Tamron 28-75, or a Sigma 24-70 is even better as has more on the wide end. Both are more flexible and you'll get better use when in ZA ... plenty to see there
Both are fast with high IQ.