I've used UPS without any issues, but you have to ship from a hub.
Since it's legally a transfer, will have to ship them to a FFL, and he will have to pick them up there and fill out a 4473 for them. So he may incur a charge for the transfer.
As far as packing, I found it easier to get a cheap plastic rifle case from the sporting goods store that comes in a cardboard outer box, and use both. I learned that UPS will charge less to ship a box containing a rifle case, than they will a rifle case by itself.
Just package it securely and have a copy of the FFL you are shipping to with you, they will need to verify that.