A few points to clarify: as Dusty said, a great shipping box is the hard plastic guncase in the manufacturer's original cardboard box - if you ORDER it online and have it shipped to you, it will come in the manufacturer’s cardboard box - there's no need to turn it inside out, just use a black permanent marker to cover any package reference to gun, rifle, or firearm. Also a couple of layers of brown shipping tape covers well.
As to shipping restrictions by the USPS, most of the ‘requirements’ previously stated apply only to handguns and other concealable firearms and not to normal length rifles and shotguns (long guns). There are two references of federal law/code that stipulate to requirements & restriction concerning the mailing of firearms; the first is:
USPS C024 - Other Restricted or Nonmailable Matter. This is the section that pertains to restricted items including firemars. Sections 1.0 through 1.7 of CO24 are applicable to handguns and other concealable weapons, who can transport and ship them and other stuff as to licensing, regulatory and enforcement agencies, ad nauseum.
Section 2.0 pertains to antique firearms.
Section 3.0 pertains shotguns and rifles and I paraphrase: Unloaded rifles and shotguns are mailable, but mailers must comply with the Gun Control Act of 1968, Public Law 90-618, 18 USC 921, et seq., and 27 CFR 178, as well as state and local laws. The mailer may be required by the USPS to establish - by opening the parcel - or by written certification that (1) the firearm is unloaded and (2) that it not otherwise restricted (not a handgun or other concealable firearm). If you read USPS CO24 no where will you find a requirement that you must notify the USPS or postmaster when you are shipping a long gun.
Section 4.0 states: Postmasters are not authorized to give opinions on the legality of any shipment of rifles or shotguns. Contact the nearest office of the Bureau of Alcohol, Tobacco and Firearms for further advice.
The second reference, mentioned in Section 3.0 above, is GCA of 1968, associated other federal law, but especially 27 CFR 178, in subsection 31 below:
§ 178.31 Delivery by common or contract carrier. (a) No person shall knowingly deliver or cause to be delivered to any common or contract carrier for transportation or shipment in interstate or foreign commerce to any person other than a licensed importer, licensed manufacturer, licensed dealer, or licensed collector, any package or other container in which there is any firearm or ammunition without written notice to the carrier that such firearm or ammunition is being transported or shipped.
Again, to paraphrase: No one may ship to anyone else OTHER than a licensed importer, manufacturer, dealer, or collector, any firearm without written notice to the carrier. In other words, if you are shipping to a FFL dealer, you do NOT need to notify anyone at the USPS.
As to what is and is not required under federal law, there remains a lot of confusion among firearm owners, common carriers such as USPS, FEDEX, etc. and also among law enforcement and regulatory agencies. Like all the other govt regulations, it was written by lawyers for lawyers - not written in common everyday language for us for whom it actually applies. For those who like reading govt legal speak, I've posted links to CO24 and US 27 CFR 178. (Enjoy). I guess you can always print them out and take them to the PO if you you're getting hassled.
I ship all long guns via USPS Priority Mail Insured and have not had any issues or losses. If you get an online USPS account and print your own labels, you do get a lower rate than when taking it to the post office counter, plus can schedule a pickup at no additional costs plus get tracking status notifications.
Hope this helps.
https://pe.usps.com/archive/html/dmmarchive20030810/C024.htm
https://www.gpo.gov/fdsys/granule/CFR-2000-title27-vol1/CFR-2000-title27-vol1-part178