Hey guys, just wondering which caliber would work best for coyotes and paper punching out to about 700 yards. I was thinking something in the .22 cal range just to keep recoil down. If it matters the gun will be built around a savage action (don't care about other action options) and barrel length will be determined by the bullet. The only other thing since I don't have the time or equipment to reload, I'll be shooting factory loads. Any help y'all can give will me greatly appreciated.