If you know somebody who owns firearms ask them if you can try shooting some different calibers. If you're just starting out i would look more at focusing on getting a deer rather than planning on making sniper shots. For longer ranges .300 win mag or 7mm rem mag would do fine. I prefer the plain jane calibers such as the .30-06 and the .270!

You can't do better than a 308 Win. Thirty caliber energy with knock down power and accuracy that is next to none. Most sniper or tactical applications are in this old, but trusted round. You don't need a magnum firearm to make long consistantly accurate shots. I don't know if it's a macho thing or what to say, I shoot a ---Mag. Big deal! Unless your after big game, I mean moose, brown bear or dangerous African big game. You don't need any more knock down power than the 30 cal. 308.
Good Hunting...