My assignment is at an airport and I work most shifts as the LEO at screening.
"Declare" your firearm however you feel comfortable about disclosing it, but make sure the agent understands what you're telling them! We've had cases where the customer was ambiguous enough about a firearm that the tagging procedure wasn't done, and the customer got blamed for it. Some airlines have you put the tag inside the gun case, some tape it to the outside, and some will just have you put it in the suitcase loose. Don't let them tell you to put it on the outside of the suitcase, though.
Use a Gun Vault or equivalent. Most gun thefts from luggage are a crime of opportunity and the metal case with cable, locked to the interior frame of your luggage, is about as foolproof as it gets. Keep your key out when you check in because they'll have you open the gun case at the ticket counter. Wheeled suitcases with the metal extending handle usually have a portion of that handle mechanism inside the bag somewhere... good anchor point.
NEVER leave ammo in the gun or even in a magazine. Use the original box or one of those plastic ammo boxes. NEVER leave a loaded mag in a gun with the chamber empty. To TSA, that's a loaded weapon.
If you have an ammo box that will fit inside your gun case, it's OK to put it in there. Otherwise, you can pack the box loose in the suitcase. I suggest taping it shut so the bullets have no chance of coming out.
Oh, an important point: Do not pack ANY firearm part in your carry-on luggage, no matter what anyone tells you! At the least, you'll be heading back to the ticket counter to add a bag to your check-ins; at worst, you'll give up the part to be destroyed. For example, I had a case recently where a guy told me that he was advised "by the airline" to put the bolt from his rifle in his carry-on, because the "parts had to be separate." Wrong!
Do it this way and you won't go wrong. I've been doing this assignment for 15 years and these tips are all proven.