CIA doesn't insure all shipping methods. Check their website
http://www.collectinsure.com/ I usually use FedEx for convenience. - have an online account and print my own labels, saves some money and time. I honestly haven't seen any real difference in service between fedEx, UPS and USPS.
Shipping cheaper long guns I put a wad of newspaper in the bottom of the box, wrap some scrap box cardboard a couple feet square around the vulnerable wrist area of the stock, then stick the stock in the box butt first so its butt is bedded in the newspaper. Then I pack more newspaper around the muzzle end, topping it with an empty tuna can so it doesn't poke through. Wrap with shipping tape a few places in the middle and cover both ends. 150 rifles, zero losses.
Expensive shotguns - I use a cheap plastic gun case - buy a few when they're on sale, wrap a few places with shipping tape. Only mod is that I think its a good idea to roll some tight cardboard cylinders, stick them in the box around the gun to keep the top and bottom parts of the cases from collapsing together when they're closed, just in case somebody steps on it.
