I would suggest something with a heavier barrel profile than a tikka that provides for less recoil also. For your age and budget I would steer you to the savage long range hunter Savage Arms
in either a 7mm rem mag, 6.5x284 or a 300win mag or WSM. If you want to get another cartridge its only $440 to get a custom barrel from benchmark (located about 1 hour from you).
here is one already setup and cheap.
Savage 111 Long Range Hunter 7mm Rem Mag Rifle : Bolt Action Rifles at GunBroker.com
trying to help a local guy out. if you want to go shoot sometime let me know.