I saw some not so correct info.
First, I am an 01 FFL (Dealer). This is what you can do:
Non FFL to Non FFL; Ship long arms only via USPS as long as they are going intrastate (within state) or commercial carrier, as long as it is within the laws of the state. Cannot ship handguns directly, must go through an FFL.
Non FFL to FFL; Ship long arms via USPS or commercial carrier anywhere in USA. Handguns must go commercial carrier only (both UPS and FedEx rules say overnight delivery only)
FFL to FFL; All firearms can be sent USPS or commercial carrier (again if UPS or FedEx, handguns must go overnight, USPS however you want)
FFL to Non FFL; if a firearm is being returned after being repaired/modified, the FFL can ship directly back to the person who sent it. Long arms can go USPS or commercial carrier, handguns must go commercial carrier. Does not have to go through an FFL unless state law says it must.
If you are going to ship via USPS, ship it Priority Mail, insured, tracked, and return receipt. This is actually a very secure method of shipping.
If you ship USPS, UPS or FedEx, have nothing on the outside of the box that says gun, firearm, rifle, shotgun, etc. You want nothing to say what you are shipping.
When shipping through the USPS you must fill out a USPS Form 1508 that the Postmaster files.
The overnight delivery that UPS and FedEx mandates are their rules, not BATFE's. The BATFE just says that a Non FFL cannot ship a firearm to another Non FFL in another state without going through a FFL.
With all of the above said, You must also take into account any state laws that must be followed. In the case of shipping to someone in CA (I am assuming that is what you meant by LA, not Lower Alabama) you must also follow the CA laws, they may (probably do) have stricter shipping laws.
Also, do not lie about what is in the package you are shipping, that could get you into more trouble than it's worth. I have shipped and received many firearms through USPS and never had a problem. I have shipped and received many firearms through UPS and FedEx without problems. At one point you may have heard horror stories about stolen shipments. These problems have been taken care of years ago (that is one reason why UPS and FedEx now mandate overnight delivery of handguns). Just make sure that you don't have anything on the outside of the box that would indicate that there are firearms inside.
Just remember that you must obey Federal AND any state laws.
Hope this helps.
USAF E-8 (Ret)
NRA Endowment Member