In my LK Knight Rifles where are a lot like your Bighorn I shoot Hornady XTP. Now they are not a real expensive bullet but they shoot well out of my rifles and I see no reason why they would not take game. There are expensive bullets out there, yes. But if your shooting 100 yards or less and don't need the big dollar bullets, many cheaper ones will do the trick. The Hornady 240 and 300 grain XTPs are great bullets.