One rifle for a beginner, of the cartridges listed in the original question... = .308! I started out hunting with a .308 for our Canadian game, and despite considerable experience since with other cartridges I have never had a very good reason to use anything else. I don't believe that as a beginner you will be able to take any practical advantage of the "more power" or "flatter trajectory" of some of the cartridges suggested previously. There are many advantages to using a commonly available cartridge that is "enough" is available in the rifle you want to buy, and is accurate, easy to shoot and cheap to purchase. I have coached many beginner hunters and have generally suggested the .308 to them. The result was not one complaint and success from varmints to moose.
As an acknowledgement to our American members, the very same could be said for the .30-06. and to our German members, the 8x57IS.
I also have also started some beginners with the 7mm08, which is the modern version of the 7x57. The 7x57 is a really nice old cartridge, but is practically obsolete. I have three 7x57 rifles and like them a lot. BUT Very few modern manufacturers chamber a rifle for that cartridge except for the rimmed version in break action single shots and doubles. Good used rifles are still on the market, but really, the 7mm08 is better than the 7x57 in all respects. Or just move up to a 7x64. Wonderful cartridge, and better than the .270 for any game weighing over 200 Kg. I base this on experience on Canadian elk and moose with the .270 and 7x64.
Please forget the .243 for general hunting. It is great for springbok and impala sized creatures, but runs out of capability with the bigger game.
Based on your South Africa location, In order of preference, the calibers I suggest are .308, 7x64, 30-06, 8x57IS, .270 or 7mm08 in that order, but subject to the rifles you find that you like, can afford, and fit you.