My recommendation if you're up for it is to wait until you're in the country to book something. I spent 2 months in a village outside Moshi, TZ and went on safari on a long weekend break from the aid project I was working on. So I had a little bit of time to get local recommendations for companies. Anything you book online now is going to be insane.
Yes, absolutely, without a doubt, do NOT book an African Safari from the US.
I worked on a few projects in South Africa for a few months some years back. After my projects ended, I traveled around for a few more months in South Africa, Swaziland, Zimbabwe, Namibia, Botswana. There are many different options and levels of luxury, but when you're looking for something from a US IP address, you only get the most expensive and luxurious options in the search results.
I went to Kruger a few times while I was there. Also Chobe, Etosha, Okavango Delta, Vic Falls, and too many other game parks, wildlife reserves, and nature conservancies to remember them all. It completely depends on how much time you have and what level of participation you want. Do you want to sit in a Land Rover and be driven around and shown nature from the truck? Or do you want to have an educational experience where you learn while you enjoy? Want someone to cook and clean for you or are you willing to wash your own plate and fork in exchange for vastly reduced rates? The vast majority of the luxury parks are like going to a zoo -- they know where the game is and their high-paying clientele demands seeing each of the Big Five or they feel they didn't get their money's worth in 3 or 4 days. So the animals are tagged and that's how they find them. Or, if you see two of certain animals together (Rhino!), you know you're basically in a zoo because that's not how they live in the wild.
By far, my favorite experience while I was there was taking a 30 day game-ranger course, learning everything about the entire ecosystem including the land, the geology, the plants, trees, soil, insects, birds, mammals, survival skills, animal behaviors, etc. To me, this was so much more valuable and memorable than sitting back and watching animals stroll by. When you have 30 days, things go much much slower. You're not viewing large game every second of the day. And much of the time you're walking and hiking. Looking for clues so you can track wildlife. I really felt like I was part of nature and the land. I was one of the few people in my class with no plans to become a game ranger, so I didn't plan to participate in any of the "exams", and I didn't care at all about bugs or birds, but when I started to understand the interdependencies of the entire ecosystem, I understood life on the African Savannah so much better and could take away so much more - and then I got competitive and joined in on the exams!
For example, did you know that AntLion Larvae are nocturnal, so if you see their very distinctive trails over/through lion tracks, then you know that the lion passed through before daybreak and is probably long gone by morning, but if you see grass-yellow butterflies floating around a scattering of giraffe dung, that giraffe can't be too far away, because the butterflies get their moisture from dung -- and you need fresh dung for moisture. I didn't learn these as factoids, I learned them because at the end of the course, I had to guide the team around in a Landie and find interesting things to talk about for 40 minutes. I needed to know what kinds of animals I was likely to find in different habitats and what clues to look for so that I could find animal that would be interesting enough to keep people engaged.
http://www.ecotraining.co.za/It's not terribly expensive, and they offer a 2-week course for people who can't spend a whole month.
One other thing I did was I took a 20-day Adventure tour with Nomad.
https://nomadtours.co.za/this-year/cape-town-to-victoria-falls-north/#itinerary It cost about $1000 for 20 days and nights, all food and lodging included, and I had to put together a tent every night (but they supplied it and a camping pad for comfort) and I had to wash one plate and one fork every day. I went 4-wheeling on the massive sand dunes in Namibia and the very next day I saw penguins!
So bottom line -- figure out a way to spend more days there than you think you can afford, then figure out what to do while you're there.