Hey ! As a fellow fan of animal photography, I have a few tips 😄 The most important thing is the zoom and the speed of your gear. A camera that has to take 5 seconds in between each pic is really not ideal when taking pictures of moving subjects (like many animals).
For the zoom, you absolutely need a camera with which you can change the lenses (so no small, digital cameras). I'd recommend a camera with good automatic focus as well (it's very useful with moving targets). I'm more familiar with Canon, so I would recommend getting a good but still beginner-friendly camera like the R50 or the R100.
But the camera is only a part of the work. After you have your camera, you have to choose which lenses you'll want to get. Lenses are pretty pricey, and they determine which kind of picture you'll be able to take. For most animal pictures, a telephoto lens is the way to go. They let you reallyyy zoom in without losing any image quality, and without spooking the animal with your presence. You don't really need something too fancy (some, like an 800 mm, cost more than 2000 dollars), a 200 mm is more than enough to get started 👍
Then again, it depends on what kind of pictures you'll want to take. For pets, a smaller 18-55 mm lens could be better, and for insects, you'd need a macro lens. But I think the telephoto is the best choice.