Second on the USPS, that guy I liked in Alamo told me once that he just filled out a form and brought a license copy with him to the PO and that it was routine. I never had to bring him packing materials since he did a lot of transfers, but that's another thing you can do easily to help out the FFL.
If you want the cheapest, usually standard priority (non-flat rate) is it. I usually went with medium flat rate though, made shipping cost predictable for the auction (I only sold on GB, I liked the format) and I could pre-pay my FFL to help keep the arrangement simple for him too. I thought it was worth spending a couple extra bucks for simplicity, everyone gets to make that kind of call for themselves.