Well, like other members have said, a .243 would be better, but even a bigger caliber won't make a difference with poor bullet placement. I'm not a crack-shot by any standard, but I can hit where I intend to. I use a Smith & Wesson .222 bolt action often while deer hunting. My first whitetail was shot with that gun from about 75 yards. One shot and he ran about 100 yds and died. BUT back to the original question, yes, buy a .243 or go bigger and get a .308 or .270. A good caliber that packs enough wallop combined with good shooting will always bring down your game.
