The way things are now, I wouldn't even try to carry a firearm on an airline (picture a "car search" for some reason at the airport and they find firearms, even though locked up in a case, and your looking at a BIG hassel)
If your not a member, join the NRA, they have some great info on all state laws and procedures for transportation of firearms. For myself, I travel frequently across state lines with firearms (to shoot). I keep rifles stored seperatly from ammunition (ammo should be locked up), and I keep my handguns locked up seperatly as well in a locked case (I use military ammo cans with 1/8 steel welds on the side, and have it drilled so I can slip a lock on it and you can't open it). Keep in mind it can get tricky when you have a truck or suv (technicaly I believe the firearms have to be stored in an "locked" area such as a trunk) Also keep in mind it also depends what state your driving through. Stay out of Mass, N.Y, N.J, and Md on the east coast. Had a friend whos cousin was stopped by D.C police as he was going hunting, they saw some rifles in back of his truck, and like 5 HOURS later he was finaly let go after they checked each gun out (talke about a bad start). I guarentee if you call the local law enforcement for any state you travel through and ask them, you'll get a different answer each time you talk to sombody.