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It's no big deal to fly with your firearm.

Unload your gun, triple check.
Unload your magazines. It may not be necessary but it's one less thing for an unknowing TSA or airline agent to get hung up on.
Carry all ammo in the original box or a MTM-type box.
Lock all in a Pelican or GunVault type case with a NON-TSA lock.
Lock in your luggage with a TSA lock.

At the airport (may vary slightly depending on what airport, counter agent, or TSA agent.)

Declare a firearm at the ticket counter.
Fill out the "unloaded" form and place in with the locked case, not inside the case, just with it.
Take your luggage to TSA screening or follow the escort.
Let TSA do their thing. Sometimes they wonder why you're standing around until they see the x-ray. They'll let you know you are free to go or want you to open the case.

Enjoy you flight.

While I am no world traveler I have flown with a firearm several times. Southwest, Delta, AA doesn't matter. Out of Lubbock is almost a snoozer, like everyone is checking a firearm. DFW and Love are about the same. Hobby was easy and IAH I had a minor hiccup early on (a discussion about the ammo being in the same case. It can be and I was right). Orlando isn't bad and Atlanta I had to walk with the escort to the screening area. I've flown out of a couple of other airports that I don't remember off the top of my head and I haven't had any issues. No problems just a little different protocol. I've never seen any tag or other identifier on my luggage.

Ain't no big deal.