I use
my friend Andy Biggs to set trips up. He leads safaris as well as plans them for people.
The cost... $10K per person for 2-3 weeks is really good. There are different levels of cost depending on the country you're going to. Botswana is probably the most expensive, and most luxurious. Kenya is middle of the road and Tanzania the least expensive, based on my experiences. I have no price knowledge of South Africa or Zambia. Namibia is different and you do it overland, it was probably my least expensive trip to Africa.
Rwanda is probably the most expensive, but gorilla permits and accommodation around the park are very expensive. However, that money is really going to the conservation of the gorillas and to the people living near the park. Uganda for chimpanzees isn't bad.
Once you see the camps and how it all operates, you appreciate why the costs tend to be high. There's a lot of people, vehicles, park permits, food and logistics that have to be paid for. A lot of people would rather use small planes in Botswana, Kenya, and Tanzania than do it overland. Those planes are usually part of packages and raise the cost.
It also costs more if set up for photography, as there are fewer people in each vehicle, so more vehicles are needed. This depends on your size of group.
Reaching out to Andy above to help plan a trip is highly recommended, but you're not going to find much below $10K. I'm sure there are cheaper ways to do it, but it all depends on the experience you want.