So I live in South Africa, and go on a safari trip about 4 or 5 times a year.
My main piece of advice would be to book somewhere they are allowed to drive off road. So stay away from the commercial and busy National Parks. Being able to drive off road is crucial so that your guide can get you into the best photographic positions.
A private guide or a specific photo tour is a must, but my preference is a private guide.
Now where to go.
For privacy and a real wild experience my favourite is the Okavango Delta in Botswana. Checkout Wilderness Safari's camp's in the Okavango. My favourite camp is probably Vumbura Plains, but all of them are exceptional. You can request a private guide and they drive off road. For me the Okavango is the best wild experience as you can drive around without seeing another vehicle the whole day.
If you like the browner colors then Namibia should be on your to-do-list. This is one of the best countries for photography in the world in my opinion. The wildlife isn't as prolific as some of the other countries, but the sceneries and the colors are amazing. There are some nice lodges in Etosha, and Wilderness Safaris also has some good camps in Namibia.
South Africa also has some great options, and has probably the best infrastructure. In South Africa you want to do one of the private reserves that are part of the Greater Kruger National Park. Ones where you can drive off road include Sabi Sands, Thornybush, Kapama and the Timbavati. All of them have great lodges, but Sabi Sands allows too many vehicles per sighting in my opinion. Timbavati is great, and I would check out a lodge called Tanda Tula. Their one guide is one of the top wildlife photographers in SA (Chad Cocking) and if you request him as your guide you'll have a great photographic experience. I was there earlier this month and had him as a guide and it was a brilliant trip.
The gear you're planning on taking sounds perfect. You definitely want fast lenses, as most of the best sightings when predators are in the early mornings or evenings when light isn't great. For wildlife you'll mostly be in the 200-500mm type range. The guides get you pretty close to the animals.
All the lodges should have electricity and WiFi.
Hope this helps, and I'm sure you'll have an amazing time wherever you go.
