It is never worth risking your life over a good photograph, leave that to the committed professional who gets paid a lot of money to do just that.
No where is this more important than in the area of capturing wild animals with your camera.
Take your time and be very patient, with a lot of luck you will be rewarded with that one great shot.
Here the telephoto lens comes into its own, allowing the ability of a close up without the danger of shuffling up close to a hungry lion.
Forget nighttime conditions during the day are ideal for photographing animals in their natural habitat.
A faster shutter speed is better if your camera has one. Just like every other form of photography practice is everything and you will have some great subjects to practice on at home.
Cats and dogs can be a great first step to going out with your camera on Safari. You can study their movement and characteristics, and do lots of takes on a moving animal until you perfect the art well before you are face to face with an elephant or antelope.
Practise using the zoom and faster shutter speeds, pretend you have to be silent to avoid the cat running off in fear. Domestic pets are the ideal subject for hours of practice and you will be honing your art with every step.
Unfortunately zoos are often surrounded by fencing which makes it very awkward to get an animal in clear view for a picture. However open wildlife parks are just great for towering giraffes and cheeky monkeys.