I second all the votes for Ruark's Horn of the Hunter. Best entree to Africana hands down.
If you're interested in diving into the deep end, I recommend picking up a copy of Kenneth P. Czech's Annotated Bibliography of African Big Game Hunting Books (1785-1950). This more or less covers the Golden era of African safari literature:
It also includes convenient summaries of each book's subject matter:
In addition to Ruark, I really like the books Chronicles of an African Trip and Chronicles of a Second African Trip by George Eastman (founder of Eastman Kodak) the first book was distributed as a gift to his employees. The second book was published recently after his notes and letters of the second trip were rediscovered by his museum.
Another good one is Denatured Africa by Streeter- a humorous telling of a safari in Kenya.
For a good story of some more recent hunting, 70s-early 2000s, I'd recommend the two books by Steve Christenson released by Safari Press. First tells of his pursuit of the Big 5. Second book tells of his efforts to bag all of the spiral horns, as well as an unguided exploratory hunt in Angola. Titles are "From the Okavango to the Plains of East Africa" and "From the Congo Basin to the Highlands of Ethiopia" respectively.
And two final suggestions, since I saw
@Sthoko posting some German books: First, Wilhelm Kuhnert's book "Im Lande meinere Modelle," which in addition to featuring many of his wonderful paintings and sketches, tells of his time in Africa hunting and sketching the wildlife.
And a final German recommendation is for Kai-Uwe Denker, famed Namibian hunter of big tuskers, "Entlang des Jaeger's Pfad." Also occasionally available in English "Along the Hunter's Path."