Hi Eethan,
For Botswana travel in November, usually the first week sells out first. The reason is because almost all safari lodge chains shift their rates from high season to shoulder season on November 1. Some lodges ease into it by eliminating specials and such in July through September, re-introducing long stay specials in October based off high seaons rates, then dropping the rates on November 1.
The animal viewing in Botswana stays exceptional until the first heavy rains which is not normally until December.
Like the others said, if you provide your preliminary budget I may be able to give some very specific advice. I have been to the majority of the upscale safari lodges in Botswana but very few of the budget ones (<$400 per person per night).
Safari lodges in South Africa are usually the same price year round. I know for a fact that every Singita lodge in South Africa is sold out from Dec 20, 2017-Jan 2, 2018. But, this is one of the most expensive places in the country. You can almost always find space in November at this point in time at most lodges.
Craig Beal - owner - Travel Beyond