I travelled with my cat - two hour flight, four hour holdover, then finally, a six hour flight. YAHOO!
I reserved my plane tickets, told them about the cat, and that I wanted to keep her with me the entire time. The reserved a window seat for her. Lucky cat.
Took her to the vet, got her certificates. The vet did not recommend any sedatives - she said they were unnecessary if I was keeping my cat with me.
Check out the airlines guidelines for bringing a pet aboard. They have certain restrictions for carriers. I bought a decent vinyl and mesh carrier, big enough for my cat to turn around and lay down in. You need to make sure the cat cannot get an arm out of the carrier in most cases, and the mesh carrier was great for this. The carrier must be small enough to fit under your seat. The stewards allowed me to set the carrier on the seat next to me once the flight got under way.
Bring treats, blankets, toys, a food dish, a small baggie of dried food, and a water dish. Bring bottled water. Incidentally, if you tell the stewards that you have your cat with you, they may provide you with water free of charge.
When you can bring the carrier back out from under the seat, speak reassuringly to your cat. My girl meowed a few times, but was otherwise okay. Mostly, the poor thing just wanted out. I couldn’t wait to set her free.
If you have a connecting flight, and have to wait a bit, I would recommend, several weeks before your trip, getting a cat harness and leash. Train your cat (gently and patiently! but it can be done) to get used to being walked. Leave the harness on for a while, let her get used to it, then add the leash, then slowly coax her into walking. She’ll get used to it. This was wonderful, because while I was waiting the four hours for my connecting flight, I could attach her leash and take her outside so she could do her business. That’s a long time to be cooped up without a bathroom break!
My cat didn’t eat much during the whole trip, slept a lot, and was ever greatful when we finally got to our destination, where there was a fresh litterbox awaiting her (courtesy of the friend (who later became my husband! :eek: ) I was visiting). Leave her carrier out and open when you get to the new place, because she might need a “safe” haven among all the unfamiliar stuff. You’d think she wouldn’t want to see the thing again, but it’s something she knows. And let her be, unless she asks for attention - she’ll want to do some sniffing around all on her own, without intrusions. She probably won’t want to be held or snuggled or smothered to bits after that long trip, she’ll want to stretch out and figure out what the hell just happened. 
All in all, my cat survived the trip better than I did, and though she had a few moments where she cried a bit, I just stuck my fingers in her carrier (through a zipper on top) and spoke to her gently. Familiar things being nearby will go a long way towards comforting kitty. The noises may scare her a bit.
I wouldn’t dream of shipping my cats with the luggage. No way, never. Having someone they know and trust nearby is the only way I’d go. My cat is scared to death of strangers, so as long as she saw/smelled me nearby, she allowed customs and airport inspectors to handle her (and coo over her and tell me how soft her pretty fur was :smack: )
She adjusted excellently, and by the next day was the reigning Queen of her new domain. Later on, when we adopter her younger sister, she showed her around the place.