Carroll......
Husband and I went to South Africa in 2015....I planned it with help of a SA specialist I found on another site because I too was overwhelmed with the vast amounts of knowledge and logistics to learn. We did not do 3 countries but targeted Johannesburg as a must as well as Kruger National Park and Cape Town.
With the help of Dave ( my specialist) we were able to put together an independent itinerary that allowed us to choose our lodging in all of our destinations as well as as any specific tours of interest in both Johannesburg and Cape Town. Our primary intent was for seeing the animals and because we used a specialist on the ground in SA, we were able to take advantage of deals and discounts he had knowledge of - enabling us to stay in beautiful lodging in private reserves which bordered Kruger....there is no fencing....the animals roam where they wish. Game Rangers are your guides while on safari and they spend 3-4 hours in the am and 3-4 hours in pm with you in a Land Rover with perhaps 2-4 other guests on a game drive. All meals and drinks are included. Another plus we had was we paid Dave directly in South African Rand and NOT US dollars and so saved a fair amount of money which allowed us to splurge for either more luxury or interesting tours in the cities.
Dave arranged all transfers between lodges and airports and we chose our own international and domestic flights.
I could go and on but I can not wait to return to South Africa and I would encourage you to not be afraid and just do it!
OAN......I can also go on and on about travel in Israel as we have been there 5 times in the 1990's albeit not as tourists but as mental health professionals. Our travels there were primarily to the Gaza Strip and the West Bank and this was during the 1st Intifada. We were able to meet with, speak with, interact with both Palestinians and Israelis in an effort to understand the cultures.
As other have said.....the news is always worse over here (US) and a different experience once you are in country. I also would not hesitate to visit Israel and you should go if that is on your wishlist...do not be afraid.
I'd be happy to answer any questions should you have any.