Currencies and Payments
Each country in your itinerary has its own currency but, for practical purposes, you don't need to worry about the local currency at all because the safari industry operates in US$ - any additional costs that you incur can be paid either by credit card or in US$.
The one exception to this rule is South Africa, where you may need some Rands for cab fares and incidental purchases (more information below).
Credit Cards
Visa and MasterCard credit cards are generally accepted, and represent the most convenient method of payment. Even in wilderness areas most camps and lodges can take payments by credit card for "extras" such as curio purchases, spa treatments, etc. In most cities and towns all expenses (including tips at restaurants) can be charged to your Visa or MasterCard. American Express credit cards can also be used, but are less readily accepted.
Travelers Checks
Travelers checks have limited application in Africa - they can be exchanged for cash at exchange bureaus at major airports, or commercial banks, but NOT at safari camps/lodges or hotels. Travelers checks can be useful as a backup source of cash (consider taking roughly $200 per person in travelers checks), but please bear in mind that they can only be converted to cash at official exchange bureaus or banks.
Cash
Please refer to your cash and tipping guidelines for the recommended amount of cash to take with you on safari.
While traveling in South Africa it is a good idea to have some Rands on hand for cabs and other small expenses, or if you are self-driving and will need to purchase gas (gas stations in southern Africa do not accept credit card payments). ATMs are to be found in most shopping malls and banks, and will normally accept Visa, MasterCard, or American Express credit cards (provided your credit account has a cash withdrawal facility). Both major international airports (Johannesburg and Cape Town) also have ATMs, and you can withdraw money as soon as you land (generally at a better exchange rate than if you were to exchange cash or travelers checks). Ideally, use a credit card to draw cash from ATM machines, if your card supports this function. If you use a debit card for ATM withdrawals, please make sure that the account linked to that card doesn't have a significant amount of money in it - if the card gets compromised, funds can be fraudulently removed from the account very quickly.