Obviously, don't fly out of NYC, they will probably arrest you and confiscate your firearm.
I use the Link Removed. Be sure the pistol is fully cleared empty. Triple check. TSA ammo storage requirements are satisfied by having bullets in the pistol magazines inside the same lockable case.
Something I have done many times that expedites getting through a long line at check-in is I go to the SkyCap desk outside (if there is one) and tell the SkyCap "I want to declare a firearm" and I immediately tip the SkyCap $5. SkyCaps can't check a firearm so they will walk you directly to the front of the line at the airline counter inside avoiding the long line. Great use of $5 in my opinion.
At the Airline counter they will ask you to fill out a simple card that declares that the firearm is unloaded and relieves the airline of liability for your possession of the firearm. Sometimes they ask you to open the locked case and verify that the firearm is unloaded but most of the time they have just had me fill out the card and put the card inside the locked pistol case. They will put nothing on the outside of your luggage indicating that a firearm is inside. Take a TSA approved lock to lock the outside of your luggage if asked to do so. The airline will then take your bag (or ask you to take it) directly to a TSA agent who checks the case and luggage while you wait there. I prefer a key locked pistol case and then I keep one key on my key-chain and an extra in my carry on bag. I use a TSA approved combination lock on the outside of the bag with the pistol case in it only if I am requested to do so by TSA.
By far the most gun friendly airline I have encountered is Southwest but all airlines should transport your properly secured firearm. Check each airlines website for their firearms policy details.