.264, most here are saying the .243 is fine for Elk and many of them have far more experience than I have but I still strongly disagree. Of course the caliber with the right bullet placed perfectly when close up will roll any elk that ever walked. That does not mean a .243 is an Elk caliber! What happens when the range isn't so short, the angle perfect, or you just plain screw the pooch and put that little bullet in the wrong place? It can all happen with bigger calibers as well but you unquestionably have more "slop in the system" with something bigger if things don't go like the textbooks say they shood. I don't know about you, but Mr. Murphy is always looking over my shoulder. I don't always get the perfect angle (read never) or the short shot, and thought I hate to admit it I have made a few shots that were less than perfect. An expert hunter capable of getting very close and putting the bullet precisely where they want it may find the .243 workable but I doubt any kid qualifies. In my opinion low recoil is simply not a sufficient excuse for using a marginal caliber like a .243. Many may disagree, but regardless of the game being hunted, ground hog to elephant, the hunter owes it to the animal to use enough gun to get the job done under the worst circumstances reasonably imaginable or stay home.
