Purchasing a gun for someone else is called a "straw purchase" and is generally illegal - that is, YOU cannot give money to your parents, and have THEM use that money to buy YOU a gun. They must buy the gun and give it to you as a gift. Of course, you can be right there for the purchase, and you should be.
Check your state laws. You could also ask a gun shop owner. If they are 'on the level' they will know your state gun laws.
In short - in the USA you must be 18 to possess (meaning to own or carry) a handgun.
You must however be 21 to purchase a handgun. Your parents can buy you a handgun and give it to you as a gift, and it is yours to keep, as long as you are at least 18 years old, not a felon, not crazy, and not a domestic abuser.
Why not ask your parents to accompany you to a local gun shop? Talk to the shop owner and try out a few handguns. Shop owners want to make legal sales happen, and if you're 18 and not in trouble, you should be good to go. Hope that helps, good luck!