Target shooting can best be done with a semi-auto .22. It's cheap to shoot and that equals fun. Most indoor pistol ranges allow .22 rifles.

As for hunting it depends on the game. No caliber has taken more game than the ancient 30-30 round in old fashioned lever action rifles. Wooded terrain and brush are great for the slow 30-30 round and other big slow bullets to stay on track after encountering small branches and twigs. Hyper fast rounds in the below 30 caliber group often disintegrate or change course as they brush vegitation making you miss.

.30-06 or similar ballistics will take down anything in North America at medium and long range.

Stay away from mid range cartridges like the 5.56 and 7.62 unless you're just playing around with prairie dogs or similar small game.

I trained on the M-14 and M-16 but used the 16 in the field. I wouldn't want to be limited to just 5 rounds for the safe bringing down of any big game. Remember most locales limit you to 5 round mags so you have to have a wooden block in the magazine. You can't just load 5 rounds or Fish and Game will get you. Also get a license and hunt for the prescribed game only in season. You can't drop a black bear with deer tags just cause he wandered in front of you.