Placing a handgun in your luggage used to be an issue, as they would place a label on the outside of it to alert airline personnel (baggage monkeys) to be sure and open it and steal the gun.
Now they no longer label your luggage if it contains a gun. There is still a possibility that your luggage may get rummaged through later (illegally)but it would be completely random.
The one piece of advice I can offer is do not ever put a gun in your luggage and not declare it. They will check, and they will find it, and it isn't pretty. You can find all the rules on the FAA website as far as the case/lock/ammo issues.
One extra thing that I do is use a pelican case (which of course is lockable) and I then lock the case to the inner steel tube frame of my suitcase (soft backpack style with wheels and collapsible handle) using a small diameter chain and extralock. This way if someone opens my suitcase (illegally) the gun case itself is not removable unless the lock is cut.
The last few times I've flown I have had favorable comments from NSA personnel, asnone had never seen a gun case locked in to the luggage. Just remember to have the keys in your pocket, as they MAY want to open the gun case when you are checking your bag.