It's been a few years since i flew with a handgun, but i seem to recall that the case must be hardside, lockable (do not use TSA locks, you MUST be in their presence if the case is opened. Had to fight with them at Cleveland Hopkins over that.) and have one solid hinge, not several small hinges.
The ticket agent will probably tell you to place the "Unloaded Firearm" tag on the outside of the case. Don't. It goes on the inside and has a metallic tag in it. X-ray screeners see the tag and know the firearm has been properly checked.
Download the TSA regs and the airline policies. Read them and understand them. Print them out and put them in your pocket because at some point in your trip, someone employed by the airline or TSA will tell you to do something against either the law or carrier policy. They're not trying to entrap you, they just don't know any better because most of them are not familiar with actual law or policy, merely "we always do it this way". Of course, some are buffoons, but thankfully the minority.
I have never heard anything of the sort and I have used containers that did not have one solid hinge