Although somewhat dated Robert Ruark’s, Horn Of The Hunter, is a traditional read for first safari. It is about Bob’s first safari with his wife. A tented hunt, unlike a South African ranch/lodge trip. Both still capture the uniqueness of Africa
I don't think I've read any Capstick but I know he is well recommended
Hemingway is an easy choice, wrote about Africa a lot
But the top choice to me, like others have said, is Ruark. He wrote this piece called "Leopards Are Different" for F&S in the 50s, really love that story
Since you asked specifically for a list:
Death in the Long Grass - Capstick
Green Hills of Africa - Papa Hemingway
Horn of the Hunter - Ruark
The Perfect Shot by Kevin Robertson is a great read for anyone going on a Safari, gives you some details about all the species and has illustrations on shot placement