If it was Namibia, I would go with one of the .300 magnums, 8x68S or .340 Weatherby (if you already shoot one and like it).
If it was SA, Zim or Zambia, I would go with a .30-06 (with at least 180gr Swift A-Frames) as a minimum; .338 Win Mag, 9,3x62 or .375 H&H. A double 9,3x74 would be another fun way to go.
These are obviously generalisations - if it was a hunt focusing on one specific animal and other incidental species, I would choose the most suitable rifle for the size of animal and terrain. If the primary species sought is sable, zebra, eland or gemsbok, I would tend towards the larger heavier bullets, but that definitely does not have to mean faster - only go faster of the terrain is open.
JMHO - in general, there are few poor choices over .30 cal for a wide spectrum of plains game.