Please try to avoid double posting.
I have never used armlist.com, but I have used GunBroker.com and found the process simple.
Gun transfers, especially those across state lines, are best handled through a licensed dealer. The buyer sends you a copy of his dealer's FFL, you ship the gun to the FFL licensee via FedEx overnight, and the FFL licensee accomplishes the transfer for a fee.
I believe that one does not need a license to ship a firearm to a licensee, but I could be wrong. Your buyer's FFL licensee will know the answer to that question.