Kate,
From one (unpublished) novelist to another welcome to the forum and, as others have said, kudos for doing your homework. I have a few comments which I hope will add to what others have said:
• This is an internet forum and the posts (including mine) may not be entirely accurate - take the general knowledge offered, but back that up with unimpeachable sources. For example, from a previous post:
<<No, a handgun is a handgun is a firearm. You can't buy a firearm without a background check.>>
This statement is incorrect. In most states it is perfectly legal to buy a firearm
from a private party with no background check and no governmental oversight at all. An individual can answer a classified ad in the local paper, go to the seller's home, hand over the $$, and legally go home with the long gun or handgun.
• This website:
http://www.handgunlaw.us/ provides information on firearms laws state by state, usually with citations from the applicable state's laws as well as links to the law sources. I consider it to be very reliable.
• Your original post seemed to imply and most responders assumed that you meant that your character would buy a new firearm from a retail store and, accordingly, fill out all the required paperwork. Would your character necessarily buy a firearm that way?
As the writer you know your character best - Would he/she be more prone to buy new from a store, or save money buying used from a classified ad? What are the character's original plans for the weapon? Would it better suit the character or the story to have him buy the pistol from a store, a friend, or from a shady character in a back ally?
I realize that now I'm trespassing on your writer's territory when all you asked for was technical info from a specialty forum, but I can't help it.
Good luck with the novel, I know how hard the whole process is.