I'm also a 16yr old long range hunter, so we probably have lot of the same problems. Mainly money
I have 2 remington 700s and one savage, out of the box, the savage is great. Mine is a model 116 FLHSS in 300 win mag, then had my gunsmith install a brake.
Get a savage. Out of the box they are hard to beat. I would say get a long action savage with a varmint contour barrel, restock, use the barrel to practice and shoot it out, then rebarrel to whatever caliber you want. Get one (or more) of those shilen, pacnor, or a douglas/brux from sharpshooter supply. They are prechambered and contoured, $300-450 and you screw it on at home and your good to go.
As for caliber, since this is your first long range gun, you will want and need to practice, A LOT. I rarely go a week without trigger time, maybe once every 2-3months.
Therefore, while a fast 7mm sure is cool, it comes at the expense of barrel life. What rifles do you have right now? a .308 is awsome for hunting to 800 (if the wind isnt howling) and practice. Then for a 7mm i personaly love the .284win. Pick whichever one you like, anything that will shoot the 168 or 180 VLD at 2900+ will be pretty freakin awsome.
shoot me a pm if you need any help, im on lrh a ton and always willing to help when i can.
Finaly, where are you located? finding another local guy to help show you the ropes is a huge plus. Really improves your learning curve.