Unfortunately they didn't take many pictures of their tents. However, I have seen a photo of Fred Selous walking past a tent (though there is nothing in the photo proving it is
his tent). Fred Selous was just about the big-gamiest of the big game hunters during our period. The tent in question looked just like a tent. An unremarkable tent of the ridge variety, rather than a bell tent.
The other really famous hunter of the day was of course, Teddy Roosevelt. He seems to have favoured a large-ish ridge tent with an American flag flying from it and an awning to provide some shade outside. But I don't imagine he was typical. It would be like trying to discover how the average band gets about by looking at the Rolling Stones' tour bus and entourage.
I would just get any tent that appeals to you, I'm sure there aren't any turn-of-the-century tent experts waiting to pick apart your choices, a tent is just a tent, after all.
To my memory, the fictional character Alan Quatermain, who was based on Selous, never bothered with a tent. I don't recall one ever being mentioned in the books. He would sleep out in the open, under his wagon or inside it.
So those are some options.