As previously mentioned by Straight_Shooter, only FFL's can use USPS to ship handguns.
FFL's shipping by USPS can save money over FedEx or UPS but you must declare each package on PS Form 1508 and take the packages to the post office yourself. Most postal clerks are not aware of this regulation and may try to refuse the package.
I recommend that you first speak to USPS Regulations Division and either get a letter from them or get a direct phone number that the clerk can call. It is also advisable that you present a valid picture ID and a copy of your FFL License. Do not leave your FFL license with the postal clerk.
The reason you cannot have a mail carrier pick up is because Form 1508 must be postmarked and filed at the post office branch you are sending from. The PO is required to keep the form on file for a period of one year.
I also recommend you pre-pay & print shipping labels. That alone can save up to 15%. It also allows for the package to be insured and provides an on-line tracking number.
It is normally less expensive to ship USPS Priority mail (2-3 days anywhere in the continental US) than flat rate. Cost is based on dimensional weight formula and destination zip code. Call and request Priority Regional 2 boxes. There are several sizes. The # 2 boxes are tall enough to ship a gun in a large size plastic case. You can also get envelopes and priority stickers if you want to use your own boxes. Boxes, mailers and stickers are free but must be ordered in advance and shipped to your store.
Do not carry any concealed or open firearm into the post office when delivering a package (handguns, long guns or anything else).
Packages containing a handgun(s) should not be loaded and should have the magazine removed. No further disassembly is required. Each hand gun should ship with a cable lock in accordance with BATFE regulations.
Do not mark the outside of the box with any indication of its contents
Ammunition cannot be shipped by USPS.
Do not allow the postal clerk to open the package (in your presence) for inspection. This would technically be the same as carrying an open gun into the post office.
If you are shipping long guns, They must be unloaded with the magazine (if any) removed. The firearm does not need to be broken down any further than this for shipping. Bolts are not required to be removed from rifles.
You will need a USPS commercial account before you can use these methods.
C&R licensees cannot ship hand guns via USPS since they are not an FFL dealer or manufacture.