When I think of classic African Plains Game rifles I think of the Griffin and Howe 1903 Springfield or the classic styled Mauser sporters. Both are classics. Both can be excellent rifles. For classics, only blue steel and walnut be it American or English.
I think that you have received a lot of good suggestions. From an American point of view, the 30-06 is the classic African cartridge. European, the 7x57. With modern propellants and bullets, they are far superior to what they used to be.
There are many great options as for the container, the Winchester M70, the 1903 Springfield or a Mauser. I like all three and they would serve you well. I would say that in general, the M70 is the better rifle, excluding a custom sporter based on an Argentine 1909. My 1909 action is as tight as any of my modern rifles.
From a flat out value perspective, you can find some excellent used sporterized Mausers or 1903 based rifles that are just lovely. But you can with most of the for mentioned rifles.
My current African rifle is a sporterized Mexican Mauser Stutzen in 308. It is very Handy , I'm not shooting over 250 yards there and if I lost my ammo, I can get more there. Anyone that says it isn't enough rifle for PG is mistaken. With the right bullet within reasonable distance it will take any antelope or zebra down. However, it's a boring vanilla cartridge. I would also have no concern with a 7x57. 7x57 just sounds cool. Before the 308, I had a 1909 Argentine Mauser in 30-06, that I still have. It's just out of rotation.
My daughter also likes the looks of the Stutzen Mauser, and she will inherit my guns. So it is now a family classic.
A close friend uses a special edition Remington 700 in 300 H&H. His big medicine rifle is a 358 Winchester in a M98 platform. Both are classics. He has taken all manner of game with the 300H&H in the US and abroad.
I would not overlook the ability to get ammo in my choice.
And just to throw out another thought, this year I may take an early Weatherby Mark 5 in 257 Weatherby magnum. It's also a classic. Classic 1960 Americana.
You have lots of choices, and none of them are wrong.
Have fun!