You will haver to define if "biggest" means caliber or overall size.
You will have to be more specific. Handgun, shotgun, rifle, crew served?
Smith and Wesson 500
No, Missouri does not require handgun registration.
Depends on what you mean by biggest. There is a revolver in .600 Nitro Express, and 12 guage pistols.
JUSTICE BROWN
To legally purchase a handgun out of state, you must have an FFL dealer ship the handgun to an FFL dealer in your state.
It depends on whether you mean legally, or what is the biggest handgun available, and whether you mean handgun size, or caliber size. The largest commonly available caliber is .45 ACP, however, .50 AE is also fairly common. That said though, there is also a handgun available in .600 NE. Most states don't have restrictions on caliber, however, some may.
Strictly speaking, no. You can only buy handgun within your state of residence. However, you can pay for a handgun in another state, have the gun shipped to a dealer in your state, then go to that dealer to pick it up.
No.
It depends on your needs. In general, you should buy a handgun that fits your hand properly. Beyond that, buy a gun that meets whatever other requirements you have.
In the US, to buy from a dealer, Federal law requires you must be 18 to buy a long gun (rifle or shotgun) and 21 to buy a handgun. In some states, you may buy a handgun at 18 from a private seller, but not a dealer.
Sporting goods stores, gun stores, or gun ranges normally have handgun ammo. As an aside, handgun ammo is in short supply at the current time.