A basic AR is a 3-4 MOA rifle.
A good AR can easily be a minute gun or better with decent ammo and shooter.
the basic Colt 6920 is an excellent starting point. A LaRue or Noveske is even better but above your price point. Then again, you get what you pay for.
"And Shepherds we shall be. For thee, my Lord for thee. Power hath descended forth from thy hand, that our feet may swiftly carry out thy command. So we shall flow a river forth to thee and teeming with souls shall it ever be. In nomine Patris, et fili, et Spiritus Sancti. Amen."