I agree with most of the above posts. The longer the lens the faster your stutter speed will have to be in order to stop shake. This may prove impossible in some lighting conditions and may require some flash.
A tripod would help but may restrict your movement while tracking, a gimble mount would be a better solution but not for your pocket.
AF or MF? Depends on what where how and when. You will end up using both once you figure out what the little or big blighters are up to :-)
It’s just a case of getting out there and doing the time, knowing your subject and reading light.
Photography is getting like F1 racing. You have to spend big bucks for just that little extra step. Maybe 1 f-stop will cost you £1000 ...... is it worth it?
90% of wildlife photos can be taken on standard gear with standard lens. I find it is the person behind the lens that makes the photo.
You can always try and get closer rather then get a better lens/camera. Wait for better light, use flash (with caution).
To me it’s about waiting, watching & learning your subject.
I have shot elephants in Namibia with a 600mm lens & Canon 1DS Mk3 with Manfrotto and gimble ..... cost ... err .... £15k plus ..... photos ... mmm .... ok.
The shots that sold were taken from about 20 feet away with a 28-70mm lens on f4 Canon 5D handheld........ £2k
Learn your gear, there is more life in it then you think. Learn your subject and get them used to you being around.
While you’re waiting for them to play ball, practice your focus and learn what works best and when.
Most of all, this has to be fun. Don’t let it become an arms race of gear to try and get your shots ..... it wont work.
Happy clicking
Tom