I won a South African hunt at a banquet, basically stole it on auction and did the trip last June. I never had any desire to hunt in Africa, I did it primarily as an adventure. I only shot 1 animal, my buddy shot 3. Just to provide some context:
We flew Delta from Atlanta direct to Cape Town. Just seemed the easiest all the way around. I believe it was 14 hours wheels up to wheels down, 14.5 coming back? I had economy aisle seats. I can't sleep on planes, hate flying, so a bunch more money for a little leg room wasn't worth it. Flew an Airlink commuter jet from Cape Town to Kimberley and felt comfortable with it.
We rented rifles from the outfitter and glad we did. Traveling with them wasn't worth the work or hassle, to us.
Great you got your animal list, but remain flexible. In talking with outfitter, he said his biggest frustration was hunters (especially first-timers) arriving with absolute expectations, in the animals they want to hunt and other items.
Find out who their preferred taxidermist is. Then do your research BEFORE you go over if you want to go through them. If you have any hesitation, prepare to bring it back here. I went with a European, so I just had it done there.
To each their own... but I would strongly recommend doing some traveling before or after the hunt. We did a few days around Cape Town and also drove a rental car to Gansbaai to go shark cage diving and visit coastal parks. I hear so many people flying to Johannesburg... and honestly, I don't get it. Cape Town is safer and has more to offer a tourist, I felt. I've only been overseas once before, so this was a hell of an adventure for me. So glad we spent the extra time traveling around and it was affordable. Just a thought.
Good luck on your trip!!