Well each of us have to find their own path and discover their passion. Here is my story. I hunted the midwest when I was your age, I loved hunting but I never was big on shooting. When I was 20 I moved to Alaska and hunted and shot everything you can here, but once again it was the hunt that was my passion and not shooting. All this time I would travel to travel to Minn for deer gun season with the family. My brother would hunt with us for a day or so and that was it because he was into archery hunting and didn't enjoy the gun season much. Fast forward about 30yrs and I go down there before gun season and my brother talks me into an archery hunt. Sure enough I go out the first day I held a compound bow and shoot a nice doe. So I bought my own compound and shot it enough to be able to shoot and kill and 35yrds. Once again I enjoyed the hunt and not the shooting. Then a few years ago I get a wild hair and bought my first longbow. Now my passion to shoot is equal to my passion to hunt.
There would be nothing wrong buying a rifle and learning how to hunt first and then take it to the next level and get a bow,especially at your age. If I had to do it all over again at your age that's what I would do. Rifle hunt a couple of years and then get a trad bow. I loved my 22 when I was a kid, it got me in the woods and I shot everything that moved(and ate it), I learned alot about hunting just being in the woods and being observant.
There are many inexpensive great used recurves under 200 that you could hunt deer with so don't let that stop you. I would not buy a new bow as you are likely to out grow it pretty fast at your age. Have fun making the decision,life is full of them.-- Steve