.300
The question is a little difficult as plains game covers many different size animals, different skin thickness and different body structures.
I prefer to use enough gun and would favor something with a little more knockdown power that one that is too light.
My preference on most of the large plains game animals such as Eland, Zebra and Kudu would be the .416. Either .416 Win Mag or .416 Rigby, as both work fine. Having used both calibers on many eland, zebra and kudu with good performance from both. Can use a .300 if you have to and if it is your only gun in the safari, but preference is a .416 on these.
For medium sized plains game, such as the different Wildebeest species, Hartebeest, Roan, Sable, Gemsbok and others of that size and structure, I prefer to have something that can reach out a bit further and still be able to secure the animal. Probably have seen more Wildebeest shot by other hunters and lost when using too small of a caliber like a .270 than any other animal. I know that you can use a .270 and kill a Wildebeest as I have done it also...and you can cull them with headshots with a .270 just fine. But for the average hunter that is trying to take his trophy of a lifetime, why go under powered on a tough animal. Put a well placed .300 round into his chest and you will make the trackers job a lot easier. I have also used a 7mm on Sable and even with a good double lung shot, he still traveled several hundred yards. I wished I had used the .300 on him or even the .416.
A .375 is also a good choice and I have used it on many plains game in Cameroon, CAR, Tanzania and Uganda with very good results. I just prefer the flatter shooting accuracy of a .300 WM over the .375 on longer shots.
For the smaller plains game animals such as the impala, bushbucks, blesbok, springboks, Mt. Reedbuck I still use the .300 as it is just easier to use the same rifle for plains game. Although for these a .270 or 7mm would work fine.
For the tiny plains game animals...duikers, oribi, steenbok, klipspringer, grysboks, dik dik and those size, I prefer a .243 or .22-250 but I have also still use the .300 with a solid behind the shoulder and they don't go far. Stay off the shoulder and you won't ruin a cape. Just don't hit the shoulder!
Overall you can use the .300 in all of the plains game and still feel confident that you are not under gunned. I usually use a CZ-USA Ultimate Hunter in .300 Win Mag using 180 grain bullets. Using both softs and solids depending on the game. This rifle has given me one hole group accuracy and as we all know accuracy is the most essential part of this whole equation.