I always tell newcomers to focus on the experience they want first, then the specific animals, and finally the outfitter / PH.
There is no question that RSA has the least expensive hunts, and a huge variety of animals. However, this is because (in most cases) the animals have been farmed from introduced animals, and raised to be hunted. Think hunting some of the very nice Texas exotic ranches. This RSA hunt is what most people do for their first trip. (Myself included.)
If you pick an outfitter and give him a list of animals like you stated above, you will almost certainly travel to 3 or more ranches to hunt various species on different days. Several of the animals on your list are very rarely found on the same ranch. This can be very productive, but for some it detracts from the "wild" experience. Ranches can be relatively small (maybe 10K+ acres), perhaps an hour or two apart on the highway, and game densities high. Success rates are very high.
You can also expect to find very nice camps in much of RSA, and perhaps some days trips to national parks, city shopping, etc. For families, this can be great.
Another option is to pick an entirely different experience, say plains game hunting in Namibia or Zambia, for example. You are more likely to hunt a single property in these countries, some so large you will likely never drive from one end to the other in a single day. (well over 100K acres). In many cases you could hunt 90% of the animals on your list on one ranch, but probably not all. Is the list really important, or the experience? Camps are often great here as well, but probably remote from towns and other "attractions".
I do think talking to outfitters at DSC or the HuntExpo is helpful. You get quite a different feel for each PH. I don't recommend SCI when shopping for plains game hunts. Wrong crowd.
Feel free to PM me with additional questions. I am going on my 12th African safari this summer with my wife. We've done each of the options mentioned above, including some far more specialized and exotic hunts (elephant, leopard, etc.). They all have their charms, but each experience is different.
Bill