A .270, .308 or 30/06 will take any big game animal in America with correct shot placement. Personally I wouldn't want to test that theory on a Grizzly Bear but its been done. For coyote/deer/light recoil the .270 may be your best choice. You can always have a muzzle break installed to manage recoil. If you don't want to spend a lot of money but still have an accurate rifle check out a Stevens rifle. @$400 minus the scope.
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Originally Posted by Ducktrickster
Being a novice rifleman, I would be nervous to shoot the 270 at live game because I can only group about 10 inches at 50 yards. Not sure what causes it but I have no confidence with that 270.
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Flinching. You are probably anticipating the recoil. Go to the range with a buddy and have him load your rifle. Have him watch your reaction to the shot. Tell him that sometime during the shooting session to not load a round and see how much you flinch when you pull the trigger. Another thing to do is get a box of reduced recoil rounds and try that. If you are not flinching and still shooting that spread have the rifle and scope checked out by a gunsmith.