bambam, now that you've answered a few questions I and others asked, I'll chime in again, echoing what others have said to a large degree and will reiterate starting off with a good .22 for initial safety & marksmanship skills and the overall enjoyment and confidence they bring to the table.
Take a Hunter Safety Class of course.
Hopefully do some squirrel or bunny hunting with the aforementioned .22lr. Helps with developing an eye for moving targets that are pretty small, or small targets that are still, both can be hard to find due to their coloring... which as you'll find out, deer hunting share and have much the same issues, albeit a slightly larger target, but you'll be shooting at a 6"-8" vital zone on old Bambi anywhere from 15 yds away to a football field or two apparently. Read up and learn about the animals a bit. Always helps to know where to place the bullet.
Others here have given excellent advice on bolt action vs lever vs semi and choice of caliber and glass, so I'll defer as there is little I could add that differs.
I will say this... as a kid I learned to shoot my Dad's 1903 Springfield which I liken to a 12 ga in terms of felt recoil. Recoil is not a problem per se, when one has developed good habits. For the amount of moola you would have put down on an AR in .308 w/ optics, you could conceivably buy a .22, a 12 or 20 ga and a used or new .30-06 plus some good glass for the .22 and 06 and with that trio you'd be set for pretty much anything that walks or flies and tastes good.
I hope you learn to love hunting as much as I and others do. Even if you get skunked (and you will), it's not about the kill, more about the love of nature and being outdoors. It's certainly a different pace than city living with its fast paced movement. Some critters, like deer, tend to move slowly until they need to boogie and boy howdy can they scamper. You can pass on shots and should at times. (the old confidence in yourself and your rifle thing)
Hunting for your rifle... enjoy the stalk, learn more about your quarry. You're already asking the right questions and being steered in the right direction by good people who know. Go slow at first until you find the one. There's a lot of choices available, each has their own quirks, fans and foibles. What is right and tastes good for me isn't always what you want or need or suits your tastes.
But the hunt...be it for firearm or critter, that IS the thing. Good companionship always makes it better.
and be safe...