Start with the camera you already own
Before you spend anything, go out with what is already in the cupboard. A ten-year-old crop-sensor body with a kit zoom will teach you more about wind, light and animal behaviour than any new purchase, and those lessons transfer to every camera you will ever own. Shoot a month of mornings in your local park, churchyard or garden. Note what actually stopped you getting the picture. Was the animal too far away, was the light too dim, or did it bolt before you were ready?
Only the first of those is solved by gear. The other two are solved by timing and fieldcraft, which are free.