Most safaris are expensive. Airfare is one of the big bites to chew off, there being fewer bargains to Africa than to more tourist-beloved destinations such as Europe or Asia. Generally speaking, the high season (and best time to travel) in the African countries bordering the Mediterranean (Morocco, Tunisia and Egypt) is in winter, the low in summer, and shoulder seasons as customary in Europe. South Africa follows the South American pattern, its summer being our winter and vice versa, and their high season being their summer (our winter).
If you can arrange to go then, January and February are best in Northern and Eastern Africa, as it is hot and dry, so you can concentrate on your sightseeing, and in the East, safari pleasures, especially filming wild animals or spotting them in their original settings. The long rainy season in East Africa is from March through May, the shorter showery period running from October to December. June through September, then, is the second best time to go. In Northern Africa, there is very little rain anytime of the year.
In Southern Africa, the best time of year is their summer (our winter), with the other seasons being reversed, too.
To most travelers, Africa means a safari, where it is now required that you do all your shooting with some kind of camera, not a gun (though the latter can be arranged, too, if you have the heart to make some species even more endangered than it is already). You can pay through the nose for a luxury safari that includes hot water showers, air conditioned tents, gourmet cuisine and the like, or you can go on less expensive tours, with protection, good tents, covered latrines and ample food. You can even go barebones, though there's no need to do that unless you really want a Spartan kind of program. The best safaris are in South Africa, Kenya and Botswana, though they can be found through much of the rest of east and South Africa. In the north, you come to experience the Arab way of life and the influence of Islam on the countries and peoples there. In the west, the tourism industry is less well developed than in the rest of the continent, with consequent difficulty of getting around there. In short, you go to Africa to see the outdoors and be a part of it. Indoors people should save the few museums there (in Cairo and Capetown, most notably) for that seldom-seen rainy day.