Look into the 6.5mm cartridge class for 1000 yards the ballistics are much cleaner.
Go the ranges that hold the competitions you want to participate in and see what calibers are doing the best. 6.5X47 Lapua, .260 Remington, 6.5 Creedmoor etc use considerably less wind, recoil less than the .308 Winchester.
Some people have problems with the .308 going subsonic before the targets at 1000 yards doing goofy inaccurate things as they transition.
The Armalite will have a 26" barrel which is good, and with a healthy dose of a stick powder behind a VLD or Sierra bullet 175 grains or heavier will give enough velocity to get 1000 yards above the speed of sound.