Good for you.

Check out a Savage bolt action in .308 if you are liking bolt actions. They are reasonably priced and they make a youth model. Every Savage i have shot has been very accurate. Also, you might consider a Marlin Model 336 lever action. I like them a lot, and they are not overly expensive. One in 35 Remington or 30/30 will work nicely for bears and deer.

Not sure how big you are but whatever you get, be sure to get a gun that fits. You can put a scope on either gun I mentioned.