I own a glock 19 and will be moving from Texas to Madison.

I will be taking a flight out to Madison and have been reading online about how to transport firearms. It would seem that the only requirement is that the firearm be in a lockable hard plastic case. That being said, could I just put my glock inside its original hard plastic case that it came in then put it in a lockable briefcase? I really don't want to invest the $100+ dollars in getting a legitimate case...

Also in Texas we don't have any license laws unless you want to conceal carry. I am not a concealed carry holder... Are there any documentation issues associated with traveling with a pistol?