I've got a 375, 416, 458 and a double on the way.
All I need to do now is let them stretch their legs in Africa.
Most first African hunts are usually just for a variety of Plains Game animals. Your .30-06, .300 or 7mm mag rifles are fine for the PG animals. The .375 is the minimum caliber for most Dangerous Game, but it's recoil can be a little much for 1st time African hunters, and its power isn't really needed for most PG animals.
I took a 7mm Rem mag on my first South African hunt, and it was fine for everything that I hunted from a Bushbuck to Kudu. I bought a .375 RUM for my 2nd trip because I wanted to hunt a Buffalo, and also took my 7mm RM. Taking more than 1 gun can sometimes be more touble than its worth, so I only took my .375 RUM on my 3rd trip which was only for PG, but I've shot that rifle enough that I'm even comfortable with it shooting prone. On my last 3 African hunts, 1 in South Africa and 2 in Mozambique, I only took my .300 Weatherby.
Be very familiar with whatever rife that you're taking, and practice, practice, practice with it before you go. Also practice shooting off sticks, 3 legs are more steady than 2.
Make a realistic list of the animals that you want to hunt, and bring enough $$ for additional animals of opportunity.
I like a 10 day hunt much better than 5 or 7 days, especially if you do any traveling to different properties or do any sightseeing.
A meet and greet service at the Joberg airport greatly helps getting your Firearms Permit and reduces other hassles there.