The key here is the local law. Fed law says mut be 21 to buy handgun (or handgun ammo) from an FFL dealer. Many (if not most) states allow for 18-20 yr olds to purchase ammo and sometimes even handguns from private sales/inheritance/gifts, etc.
This is, of course, providing all other local laws are complied with. If your state requires a permit or FOID to buy/posess, then you must have one, before you purchase/posess.
A 19 year old seldom faces any kind of problem if he goes to the store and buys a box of 7mm Rem mag. He can also, legally buy a box of .357mag (for his Marlin carbine), priovided he states it is for a rifle, if asked.
The key is the local laws, which variy widely. What is legal in Arizona is not automatically legal in New Jersey, for instance.
Check your local laws, and act in accordance with them.
All else being equal (and it almost never is) bigger bullets tend to work better.