There is no gun registration in Arizona, no need to prove ownership in order to carry, so no you do not need a bill of sale.
Minimum age to open carry is 18. Minimum age to conceal carry is 21.
I strongly urge you to become knowledgeable on the gun laws of your state. You could do worse then to start here and follow all of the links. Taking a concealed permit course would be a good thing too (knowledge is power) even though you are presently below the minimum age to receive the permit now.
You might consider taking college courses to earn your associate of arts degree in Criminal Justice - that would hold you in good stead should you actually pursue law enforcement as a career. You may find that you will need something to bring you even competitively with those candidates that have a military background. LE is a lot more than familiarity with guns.