I can't speak for SA/Botswana or anywhere that vehicles are allowed off road. My experience is in the large parks of Kenya where only in some small private reserves are you allowed off road - the same applies in most of Tanzania.
From pictures/videos (youtube) I have seen, I prefer the no off road approach because in those pictures/videos from off road vehicles, there so often seems to be other vehicles in the background and quite often one will approach too closely and spook the animals. I never found any vehicles in my shots because all vehicles use the same widely spread tracks so you won't often find another vehicle track within shot.
Leopards are especially shy and easily disturbed. They will move away into cover if approached too closely. Cheetahs are more of a plains animal and it can be difficult to get frame filled shots from a fixed position so a longish lens is important. Rhinos should not be approached closely. Lions take no notice whatsoever and you'll get quite close to those. Where light direction and background are concerned - well you just have to make the best of it with your allowances for backlight and shadow but remember that in Kenya/Tanzania you are on the equator, so within 1 hour of sunrise/sunset you can expect the sun to be high and its direction is pretty much irrelevant as the light bounces around off the light coloured soil.
Any African background is good but the park authorities realise that photographers want the best and in northern Tanzania/south western Kenya you will usually have the opportunity to use Kilimanjaro as your backdrop. Even in those countries that allow off-roading, you will still need the same long lenses for smaller animals and birds.
Only twice in Kenya did I see more than one or two other vehicles at any location and those were special circumstances. The first was a dedicated rhino reserve where rhino had recently been hard to find. As it happens I was using the lodge's mounted telescope from a high up ledge and spotted rhino at a water hole. I went to find our driver and our small party sped off but once we were on our way the driver let others know by radio - that's how it works and it works well and we still got 15 minutes of private viewing before a half-dozen vehicles turned up in line alongside us. The other time was when we were halted by an elephant migration crossing the track and holding up 6 vehicles - several hundred animals, so we weren't complaining.
In Kenya and I believe, in Tanzania, vehicles have to be out of the parks before dark and the African sunset/sunrise is very short so you need to be quick to get those shots.
As an aside and for the information of anyone planning a safari to Kenya - my favourite camp is an eco camp in Tsavo east. I recharge my batteries at every chance and arriving with a fully charged set and several spares proved to be wise as batteries for charging had to be handed over to the management so they could eke out their megre supplies of solar powered electricity, although the c*
y Russian panels were soon due to be replaced with a more efficient system. These low impact eco camps are inside the reserves, surrounded by a very low, single strand wire fence - not to keep animals out, but to keep people in. Animals wander past while you're having a gin and tonic, so keep your camera close.
For the OP - yes, Africa is addictive so don't count on only needing a long lens for this one trip. Why not buy a lens - new or used - and resell on your return if you feel you won't need it again - but I'll bet you keep it.
Take it from me - as much as you are looking forward to this trip and however high your expectations - it will blow your socks off and you'll want to go back.
PS. Don't forget the people and the wonderfully coloured and varied birdlife and the landscape itself, especially early morn and evening.
Vic.
That's pretty obvious. But if the horizon is covered with vehicles doing the same thing as you are doing, how do you get pictures with no vehicles in them?
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It's all about light.