I have flown several times with handguns and ammo. You have to declare the handgun and ammo at the airline ticket counter, open the locked handgun case and show them the weapon, place a provided orange tag in the handgun case, and then put the handgun and ammo is a locked suitcase. I've used both the manufacturer's hard plastic handgun cases and a NanoVault steel case. The suitcase does not need to be a hard case or metal. You are instructed to proceed to TSA Check-in and do it again, this time it's performed by the TSA agent. At some airports, an airline employee escorts you to the TSA Check-in; in others, you walk unescorted from the airline counter to the TSA Check-in area. Again, there are differences in how TSA does the check-in - in some, you are told to stay outside the security room and watch (airline employee stays with you); and in others, you open the suitcase and the handgun case, let TSA inspect it, relock it, return to the suitcase and relock the suitcase. I've transported ammo (100-200 rds) in manufacturer's cardboard boxes, no additional protection, and in the same locked suitcase. The suitcase is tagged by TSA and not reopened as it is handed over to baggage for loading.
I have no problem with the procedures - it's for everyone's protection; but I'm not clear why the airline counter wants to see the handgun first and orange tag it, when you're then simply instructed to proceed to the TSA Check-in and go through the inspection again. I would think the process can be streamlined by just declaring the handgun/ammo at the airlline counter, and being directed (or escorted, as in some airports) to the TSA Check-in for inspection.
Also, neither the airline counter person nor the TSA agent ensured that the handgun was not loaded. From one standpoint, I understand why they would not want to handle the weapon to check the chamber (both areas are not "Safe Areas", and in most cases, they're not familiar with the weapon); but not ensuring the handgun is empty seems contrary to the policy that loaded weapons may not be transported.