You can build an AR15 for around $500, so why not go that route? I recently put together a gun for a friend for $600 with an A1 upper. Before that, I bought for myself a 16" ss fluted DPMS upper for $350 from the equipment exchange. Add a lower $80, parts kit $50 and stock $40 and you're looking at a cheap VERY ACCURATE AR15. Just keep your eyes peeled on Ebay and the EE. Aren't Cav Arms lowers around $200?
Personally, i think that at your age, you'd be well served by a bolt gun. I'm glad I learned on my remington 700 PSS, because my trigger handling and shot to shot accuracy in every gun I pick up is due to those long hours on the trigger of that gun.
However, on a bolt action, you're looking at a scope, which can get expensive, so maybe an AR is better for you.