>>4468527 Yep, safaris are expensive!
If I had to do it again, maybe a 28–70 and the 180–600 mm you mentioned. Because you're using full frame and I guess plenty of megapixels, you could always crop in a little at 70mm if you had to (and use 28mm or so for the landscape photos).
You might want to think about a little pocket camera with a flash as well — useful at night around the camp (or lodge etc.).
Also, a good pair of sunglasses and some small binoculars (just looking and being at the moment is important as well).
As for how many days, that's a tricky question. The guides will know all the best places for the animals, and you could see all the 'main' ones in a few long days, but there's so much more to see. If you're going all that way, it seems a shame to rush. So my (slightly vague) answer is as many days as you can comfortably afford.