The reason I started with Animal Kingdom is because it requires the most patience. Having to deal with animals, you have to go on their terms. They aren't on a certain schedule to make an appearance at a set location on a set time. Like they say on the Kilimanjaro Safari, "no safari is ever the same". So getting an ideal image will take some time and patience, but the results will be worth it. With that being said, let's get packed for this safari and head on an adventure!
You'll hear it time and time again, hit the Kilimanjaro Safari early especially in the warmer months. Plus the animals will be getting their breakfast and in prime locations. The "colder" months, I find the animals active regardless of the time of day. With the animals being off in the distance, you'll need a lens with some reach like the 55-200mm,70-300mm, and 70-200mm. Prices for these lenses vary, so find one in your budget. If buying a lens isn't an option at the time, look places that offer lens rental.
Shutter speed is important, the ride is bumpy and they tend to move quickly. You'll want to freeze the action with a quick shutter speed like 1/200th of a second or faster. Any slower and you risk getting some motion blur.
The walking trails are a bit easier since you can take your time. The settings shouldn't change much here except for ISO. Once you enter the area with the birds, the trees block out light. So you may have to crank up the ISO level to get your image. There are so many things to see on both trails. Take your time and take it all in, too many people rush and miss out on the details.
To recap everything, you'll need a long focal length and fast shutter speeds. A tripod isn't needed here unless you plan on taking some long exposures. Fothe shows, I recommend having the camera on Auto ISO and having a lens with a constant aperture. It gets too dark and flash is prohibited, so it might not be worthwhile to photograph.
Bonus: If you want to experience the animals at a slower pace. I highly recommend signing up for the Wild Africa Trek. It's something worth the money and the food is amazing. It is something I look forward to doing again in the future. It was worth every penny!