RE: small gun bigger than .243
Fantastic comments above. I would just add that if you will be shooting at the range quite often for sporting, then i would stick to something with a little less recoil. it makes no sense to develop a flinch at your age. I think a .270, .308, 7mm-08 would be a good gun for what you are looking for. I am not a fan of the .243 but i know alot of people are. I just think you should be a very good shot or risk wounding the animal. Now it comes down to what you will want to hunt. If you are hunting just deer then the above are perfect. If you see yourself hunting bigger game later, get the more powerful caliber right away and get good with your gun thru the years. I would say .270, .308 or 30.06 would work well. I have a 30.06 and i put a recoil pad on it cuz i like to range shoot quite often. The recoil pad makes a world of difference. The 30.06 doesn't kick that hard either. In fact, i came from hunting with a 12 gauge and the recoil there was much greater. Keep in mind that most guns will kick you a bit if you are shooting from the bench all day, but you will never remember the recoil when you take game. You will forget you even shot the gun once the game falls. The bigger calibers take game better and quicker (all depending on the shot) but in case you are a little off it works well. Just my opinion.