I suggest being able to reach around 500-600mm if possible, though 400mm would be doable if you are happy to crop a lot when editing. Note that when I suggest these focal lengths I’m referring to full frame equivalents – if you’re shooting with a crop camera (also known as APS-C or DX) you can use a shorter focal length to reach these. Read here for more information about equivalent focal lengths. How you get to this focal length will depend on what you own and/or budget. Flexibility is certainly helpful as you’ll be shooting from the fixed position of a boat or 4×4 vehicle, so a zoom is recommended. Apart from game drives, there are also plenty of scenery options and something in the range of 24-70mm or 24-120mm is helpful (again, in full frame equivalent). To this end, having a long range wildlife lens and a shorter scenery/general lens is recommended.
Specific recommendations are difficult because technology is always changing with new options being released. It’s more straightforward to recommend lens focal lengths as a starting point, then you can match that with the appropriate camera of your choice. Many entry level camera packages include two lenses with focal lengths around 18-55mm and 55-200mm. These are passable but you’ll often wish you had more reach for distant or smaller animals.
Instead, for a crop sensor camera a 70-300mm lens is a better option for more reach, is commonly made by many lens manufacturers, plus it’s small and lightweight. Even better would be a zoom that reaches 400mm, which can still be had for a reasonable price and isn’t too bulky. I’ve used the Tamron 100-400mm for a trip to the Subantarctics islands and been happy with its performance at a fraction of the cost of the high-end Nikon 80-400mm.At the larger end of the scale are lenses that go up to 500 or 600mm which would be useful but those options start to get expensive, big and heavy.
Some travellers used a Sony RX10iv bridge camera which has a 24-600mm zoom lens and got great images. It was a relatively new model in 2023 but alternatives may be released over time.