http://www.nraila.org/Issues/FactSheets/Read.aspx?ID=43
"A person under age 18 may not possess a handgun or handgun ammunition, and it is illegal for a person to provide a handgun or handgun ammunition to a person under age 18, except for target shooting, hunting, or certain other exempted purposes. (Youth Handgun Safety Act, 1994)"
See
18 USC 922(x)(3) for exemptions, having to do with transportation directly to and from exempted activities, or in farming/ranching activity.
Also, you should very careful of how you structure the purchase of the firearm with your parents, so that it won't be considered a "strawman purchase" by the ATF.
Before you proceed much further, I think it would be sensible for you to consult a lawyer on these issues, as the penalties for these so-called "crimes" is significant. Penny Dean, of Concord, is well-versed on the intricacies of gun law, and would be a good person to contact.
She'd also be able to answer the question of at what age you're permitted under the law to carry a handgun, openly or concealed, in New Hampshire.