South Africa has the largest hunting industry on the African continent and hosts possibly 40 percent of the entire continent's hunting safaris. Although South Africa offers the entire Big Five, the majority of South African safaris are for plains game. In fact, with the possible exceptions of leopard and rhino, I don't recommend South Africa for dangerous game. It's a supply-and-demand business, permits are too limited, and prices for buffalo are high. But South Africa is a great plains game hunting destination.
The actual game list varies somewhat by province, but greater kudu are available almost everywhere. Gemsbok and nyala are key species, and, depending on the area, local specialties include bushbuck, Vaal rhebok, bontebok, oribi, and more. Outfitters are generally reliable, provided you use due diligence in making your choice.
The norm is a fairly modest daily rate plus trophy fees for game taken, so safari costs are pretty much managed by your trigger finger. Alternatively, many outfitters offer inclusive "packages" for a set number of days and certain animals and, if these fit your preferences, can be a great way to go.
Drawbacks: These two things should not be sugar-coated, and the South Africans need to do something about both of them. First is crime. It's been bad in the cities for some years but is expanding to rural areas. It is random and not generally directed against tourists, but on an increasing basis South Africa is a country where one should be careful. You're OK with a reputable outfitter, but I would no longer wander around with a rental car like I did 30 years ago.
Second, and this is the unfortunate truth, "canned hunting" is a creeping pandemic. Game fencing has been common since game ranching really got started 40 years ago, but today "put and take" hunting is getting out of hand. There are many great operators who don't touch this stuff, but today you need to be wary. Guaranteed trophy measurements should always be suspect, and ask hard questions about just how big the hunting area is. There are some reactionary outfitters who are specializing in free-range hunting, and in some areas, like the Eastern Cape and Northern Cape, a lot of areas are still open range.