I get to travel several times a year for my business.
All the airlines have been friendly about this. However, you must know the procedures yourself if only to direct the counter personnel down the right path. A couple have handed me the form for Air Marshals to carry on-board
Make sure you get and sign the red or occasionally, white tag to declare an unloaded firearm. The agent will ask you to place the signed form in the case your gun is secured in.
I've learned to not fight bureaucrats and to create a way to minimize my pain dealing with
them. The "ammo issue" has been the only source of confusion on the part of TSA
agents. So, I paid less than $10 for a security box from Office Depot.
It's a small (7in x 7in x 2in) metal box with a lock on it. There's room for two or three ammo boxes after discarding the plastic inserts it comes with. I place my ammo in a factory ammo box, like the one the ammo came in. Then, lock the ammo box in the security box. Since doing this, there has not been a single issue about ammo.
For the gun, I use a Center of Mass portable gun safe. It has a cable one can use to secure the gun safe to another object.
http://www.center-of-mass.com/
My luggage has metal struts inside that house the collapsible extended handle. I wrapped
the security cable around a strut inside the luggage. This adds a step to separating the
gun from the luggage. Without cutting the cable, the gun and luggage stay together. TSA
or I can open the safe while it's tethered to the luggage.
The metal box with ammo and the gun safe can go into the same luggage bag.
TSA usually wants me to unlock the luggage and the case holding the gun or ask
me for the key or combination. Lately, they've simply x-rayed the luggage
without opening it. Then, I wait near the counter for a "thumbs up" from TSA before going to my gate.
TSA has, so far, always re-locked the locks on the boxes and the luggage after
the inspection and scan.