What’s going to be really important for wildlife is moreso the lens(es), rather than the camera body.
Generally speaking, what you want out of the camera body for wildlife is fast burst shooting for capturing that action moment and fast/accurate autofocus for keeping animals in focus while they’re moving.
A good and fairly priced camera body that will do this would be something inthe Sony a6000 series, the latest which is the a6700, but you could probably easily get away with an a6600 or even an a6400. (The less you spend on your camera body the more you can spend on lenses, and your lenses will cost significantly more than the camera body).
The a6700 is $1400, you could save a few hundred going used and/or getting one of the previous models.
But far more important than that is the focal length of the lens, and the maximum aperture of your lens.
The focal length is important in allowing you to get good photos of the wildlife that fill your frame/photo by optically getting you close to the animal.
The aperture is an opening in the lens that acts very much like the pupil in your eye. The maximum aperture is how large that opening can get, which is important because the bigger it gets, the more light it lets into the lens.
Letting more light into the lens is critically important because the more light you get, the faster your shutter speed can be, which will help you freeze the animals when in motion.
An good lens to start with would be the 70-200mm f2.8. (The maximum aperture of the lens is the f2.8. The smaller the aperture number the bigger the opening).
The Sony 70-200mm f2.8 costs between $200-3000 depending on the version you choose. That may seem eye watering, but consider that you’ll be able to use this lens literally for a lifetime (provided you take care of it).
For wildlife the 70-200 f2.8 is a good lens to start with but if you get serious about it over time you’ll likely want to get longer lenses to get you even closer (optically) to your subjects.