Oh I should probably make a page about what I use on my website haha... I use a Panasonic G80 with three lenses: a 25mm for general use, a 60mm for portrait and macro, and a 100-300mm for wildlife.
My advice for someone starting photography in general would be to grab something not too expensive and experiment, find what subjects they like, learn some advice about lighting/framing/etc. For wildlife specifically, get something with decent stabilisation and a good zoom (my 100-300 on a matching 4/3 body allows decent shots). Then bring your gear with you on walks: in parks, forests, beaches, mountains, paths, whatever you got where you live. Try going out early in the morning or late in the evening. Stop in calm spots, sit down for a bit, listen and watch. And most importantly, be attentive and patient. Once you really start being careful about your surroundings, you'll start noticing animals more easily, and you'll learn how and when to see them!