A cross country move is not easy, and pets definitely complicate an already difficult situation. When moving your pets a long distance, you have two options: drive with the cat or fly. I chose flying because I decided that one day of stress on an airplane for my cat was better than four or five days of stress in a car.
I flew with Northwest Airlines that allows small pets to fly in cabin with the passengers. This appealed to me, especially because I had to make a connection and my cat was not luggage I wanted to get lost. I used an airline approved pet carrier from Pet Sherpa that cost about $60. It looks like a black duffle bag except that most of the sides are mesh to allow for air flow to the pet. The bag was very discreet, and most people did not realize that I had an animal in it. On one flight, the flight attendant actually offered to stow the bag until I informed her that my cat was in it.
The airline charged me $150 to take my cat on the flights. This was about 10 times the amount I paid for the suitcase I checked, but the airline obviously knows that a pet owner is a good target to hit up for money.
One of my greatest concerns about flying with my cat was that his yowling would annoy the other passengers. My cat is notorious for complaining about being in his pet carrier, and he will meow relentlessly until released. Luckily, when I went through airport security, my cat got so scared, he shut up for the rest of the trip. It was required that I remove my cat from his carrier so that his bag could be x-rayed. No one had warned me about needing to remove my pet from the carrier during security check, so I was quite alarmed, but not nearly as freaked out as my cat. I held on to him very tightly because if he got away, I don't know what would have happened, but I envisioned headlines like: Cat shuts down airport.
Airport security frightened my cat so badly that he was relieved to go back into his carrier where he chose to stay silent lest I take him out again and expose him to more weird situations. During the flights, I actually enjoyed having my cat with me. I could slip my hand in his carrier and pet him whenever I wanted. Being able to fly with him in cabin was a great relief to me, and I'm glad I had the option instead of being forced to send him in crate in the cargo hold. I was happy with the experience of flying with my cat. I would even do it again if I had to, but I don't tell my cat.