First and foremost, let's talk about cases.
1. TSA: TSA stands for "Transportation Safety Administration". The TSA are responsible for inspecting you and your luggage at the airport. They are responsible for setting the regulations and guidelines for anything brought onto a flight. One of these regulations states that all checked luggage must be left unlocked unless it is equipped with TSA-approved latches.
2. ATA: ATA stands for "Air Transport Association". These types of cases are rated to safely travel a set number of times on an airplane. There will be a number associated that is a the ATA rating. For example, a case that has an ATA 300 rating can travel 300 times checked on an airplane safely. This is taking in consideration the handling and conditions that are typical for air travel.
As you can see the TSA rated case is not the best option for flying. It does have the approved latches, but is not approved to actually fly. An ATA case is the correct choice as it is specifically designed to be put on an airplane and get your guitar where it is going safely. Often ATA cases will also have TSA locks.
Next we will talk about preparing your instrument for travel.
We recommend that you wrap the headstock in newspaper. This will minimize the amount of movement that can occur. Also, place a note detailing how the instrument should be repacked in the event it is opened for inspection. Finally, take any loose items out of the case and put them in your other luggage. This will help make sure they do not end up bouncing around all over your instrument.
Finally, realize that there are always risks involved with flying with an instrument but with proper preparation you can minimize them. If you have something that is irreplaceable or highly valuable (1959 Les paul, ect...), purchase an additional seat and just take it with you.
Good luck and happy travels!