18 for rifle, 21 for handgun. You can buy any gun at 18 "privately" through a friend or relative as long as they didn't buy it FOR you from a dealer.
As far as carrying, you can concealed carry in your vehicle and residence, but not in public without a permit at 21. You can also open carry (on your hip) at 21 without a permit in most cities/counties/areas. Check with your cities ordinances, and give the county sheriff a call.