Canoe,
I'm trying to think of some of the major less obviousness issues you will need to conquer and not things like shoot a bunch off sticks or take only 4 sets of field clothes because a proper Safari outfitter will wash press and fold your clothes every day, really they will. Here are some things to get you started. Read some of the recent books written about hunting Africa. They contain lots of good advice. Here are a couple I found very helpful.
"Eight Days in Africa: The Story of an African Safari" about $10 on Amazon
"Safari 101 Hunting Africa: The Ultimate Adventure: Getting There and Back " Soft cover about $15 at Amazon
The traveling and various firearms permits can be some of the most confusing issues a first time hunter traveling to Africa.
I will reinforce a point that was made earlier, make sure you use a travel agent that has experience with African Hunting Safaris. Things go wrong on flights these days and they will be indispensable in helping you get things fixed. Plus they will typically be up on various red tape issues such as rifle transfers from Airline to Airline etc.
The hardest physical part of your trip will likely be the flight(s) over. We used South African Airways last time which stops in Dakar half way to Johannesburg to refuel and change crews. Next time we will spend a little more and fly Delta direct from
Atlanta to Johannesburg.
Be very careful you understand what special Firearms permits will be required if you fly through the UK or Europe. It will be necessary to get the permits done with plenty of time to spare in case something needs to be re-done. This can of course be avoided if you fly from the US to the RSA either via South African Airways or a US carrier like Delta.
For a first timer I would suggest using a firearms permit liaison to help you through the RSA permit process. We use
Rifle Permits - In Support of Conservation Through Hunting, they are always great and your are in and out of the SAPS office in about 15 minutes. Again get this done as early as you can to leave time to fix mistakes. Something people don't talk about is how long it takes to send paperwork to the RSA. Through the best international carrier there is, DSL, it takes about 11 days. Sending the paperwork to the RSA will typically run in the $100-150 range per package.
Lets see, TSA locks for you firearms/archery case. Look on the web for long shackle TSA locks. Once you find some try them on what ever sturdy rifle case you plan to use. If you need say 3 to lock it buy a fourth one as a backup as they can get broken during transport and you can be stuck searching for another one in the airport. Not easy to fix. We even had one stick on us in Dulles once and it took some effort to get the case opened, but I had my backup lock with me.
One last thing, even though your current mindset is your not into trophies give a thought to bringing back all the stuff, hides horns and skulls. My father had a similar mindset on our first trip but changed once he got there and had some success. The point is, if you leave it behind its gone for ever. You don't have to mount anything if you bring it back, but you give yourself the opportunity.