Spook, I do not see that you have rec'd an acidic answer- yet.
For the record, I am not an attorney. I am the holder of a Federal Firearms License. This permits me to acquire and dispose of firearms in interstate commerce. Have held that license since 1976.
In addition to state laws, Federal law applies in two specifics. The original post regarded acquiring a handgun from another state. Later, the statement regarding shipping a handgun by US Mail.
I would direct you to Title 18, US Code, Section 922. This is the Federal law that governs most of the manufacture and transfer of firearms. In brief, it states that except in a very few limited cases (inheritance being one) that it is illegal for a person that does not hold a FFL to acquire a handgun in interstate commerce. That law may be complied with by having the firearm rec'd by an 01 or 02 FFL in the state of residence of the recipient. The FFL holder then follows the same procedures as if you were purchasing the handgun from them- insofar as completion of the Form 4473, background check, maintaining records of from whom the gun was received, who it went to, etc.
In re: shipping a firearm by US Mail- This is covered in the domestic Mail manual, as well as 18.922. In brief, this is a RESTRICTED mailing. A non-licensee can mail a rifle or shotgun, so long as 18.922 is complied with. However, ONLY a licensed DEALER or MANUFACTURER may mail a handgun by US Mail. This requires a certification made to the USPS. Falsification of that certification is perjury.
In general, the internet is not the best place to find legal advice. I would suggest you contact the Federal Bureau of Alcohol, Tobacco, Firearms and Explosives, since they are the agency that regulates interstate commerce in firearms and ammunition. You can find their phone number on page 1 of most telephone books.