As an Africa veteran I can vouch for Visa. It's much easier to find a Visa ATM than a Mastercard one in many countries in Africa.
Don't expect to be able to use a credit card to pay, unless you stick to the handful of big hotels and shopping malls that serve tourists. Hardly interesting. In Southern Africa cards are a bit more accepted, at least in cities and big towns.
US dollars are a good backup and you can change them at decent rates almost anywhere on the African continent. Some hotels and shops will even take direct payment in US, esp. in certain countries. Also useful for bargaining. Rands are a good bet in southern african countries.