Well with flying most liners will ask you to place the firearms in a lockable container, keeping the key on you, then you go through baggage check... The ammo can be in your carry on but the guns must be unloaded
Most liners will ask you to do that because it is required by Federal regulations.
Can't help you with GA laws, but we can cover the flying with firearms laws:
1. Unloaded gun in a hard sided case with locks that only you have the key/combo to. NO TSA LOCKS!(Against Federal Regulations). I lock the slide back to easily show it is unloaded on xray.
2. Most airlines allow ammo in the case with the gun. Some airlines require the ammo to be in carry baggage but not in the gun case. Federal regulations are silent. Federal regulations do require proper packaging of the ammo - factory box is the best and will always pass regulations. I had a 20 round factory box of ammo in the corner of my pistol case. I keep magazines unloaded for simplicity.
3. Go to the baggage counter and tell the counter person that you have an unloaded firearm in your baggage to declare. They may or may not ask you to show them the gun is unloaded. They will give you a declaration tag to sign, and place NEAR the gun case INSIDE your luggage. If the gun case is going by itself, the tag goes inside the gun case.
4. You may lock your luggage containing the locked gun case if you desire, that lock should be a TSA lock, or TSA will likely cut it off.
5. The baggage counter person will direct you and/or escort you to a special TSA screening area. They will x-ray your bag and send it on it's way. At no time are you allowed, by Federal Regulation, to give anyone the key/combo to the locks on the gun case. If TSA asks for it, politely refuse and offer to open the lock for them.
6. Your luggage with the gun in it pops out at the carousal at your destination just like normal luggage. You will probably find a zip tie on your luggage, and a note inside saying that TSA opened and inspected your baggage.