You can go to the Domestic Mail Manual on line and look it up- However-
A private citizen CAN mail a RIFLE or SHOTGUN to a FFL, or to a manufacturer for repair, and have it returned to him. It MUST be going to a FFL if crossing a state line. You CAN mail a rifle or shotgun to yourself at another address (say for hunting trip out of state). You can also mail a rifle or shotgun to a non-FFL if you are both in the same state
Live ammunition is not mailable. Period. Brass can be mailed.
HANDGUNS may not be mailed EXCEPT by a FFL DEALER or MANUFACTURER. I am an 03 FFL (Collector) and I cannot mail a handgun. When a handgun IS mailed, a Form 1508 must be completed at the post office, attesting to the RESTRICTED MAILING.
Non-FFL folks may SHIP a handgun by common carrier (UPS or FedEx). THEY require that you use next day air. Since that will run you about $65 for the average handgun, you may be much better off to find an 01 Dealer, and pay HIM to mail it for you- he can legally use a flat rate mailing box in the US Mail.
For anyone that figures they will play "Don't ask-don't tell" with the Post Office- please remember- The US Postal Inspection Service has the highest conviction rate of any Federal Law Enforcement agency.