Good stuff. Also I heard of ammo being confiscated in some cases so I also printed out the rules on it and put it in the bag that had the ammo.Here is the link to the United special baggage page: https://www.united.com/web/en-US/content/travel/baggage/sports.aspx
Print this along with the TSA rules on flying with firearms and take them with you to the airport. I have had to pull them out a couple of times, and it makes things much simpler.
Gun cases are part of the sporting equipment exemption for all of the major airlines including most foreign. Small regional airlines sometimes are a problem if they only run small planes. The charge will be for a standard checked bag. Just tell them it is a firearm, and they'll take care of it.
Here are a few other tips if you haven't done this much. I have, and it is really pretty easy.
Domestically, you can sometimes pack ammo in the same case. Internationally, NO ammo in the gun case. I usually pack it separately to avoid hassles.
Ditto on pulling the foam out of your hard case, and packing clothes in there with your rifle. I put my rifle in a lightweight soft case and pack clothes and other gear in my Pelican case with it.
Take a second set of locks for your case. TSA sometimes, for unexplained reasons, cuts them off. DO NOT use TSA locks on your gun case. Make them get the key from you to check it out.
Pack your optics and camera in your carry on if you can. The other option is your gun case for optics, but only if you can't carry them on. DON'T put a spare scope in your carry on put that in checked baggage.
If posting a link is a no-no, I can kill the link.