Should you choose Zambia, you can choose an affordable hotel in Livingstone and save money for the game camps. We stayed at Protea Livingstone, part of the Marriott chain, and were well content. Go to Livingstone at the start of the trip and save the camps for last as they are truly special experiences.
https://www.flyertalk.com/forum/marr...ls-zambia.html
Emirates flies to Lusaka. That could be an option for leaving Zambia.