I have quite a bit of experience with this, as I have sent quite a few of my 1/12 builds all over the world. I am on the east coast and I have shipped at least 3 or 4 to California.
What I have found works for me is finding a secure location under the car, a place that is solid and can easily support the weight of the entire car, and firmly fasten it to some kind of base that is strong and will not move around inside the box. For my Corvettes, I wrapped some pretty hefty wire around certain areas of the frame and secured them. I then wrapped the entire car in lots of TP(wont scratch) and then filling the box up to the top with bubble wrap, making sure the box is completely filled with bubble wrap not giving the model a chance to move. Also, before putting the car and base in the box, you will probably want to put several layers of bubble wrap in the box where the base will sit. The point is to keep any bump or vibration to transfer directly to the base/car. Once the box is sealed, I take another larger box, fill it with packing peanuts until there is about 3" of peanuts at the bottom, and put the box with the model inside, and then fill the larger box with more peanuts around the sides and top. Then seal the larger box and ship.
All that said, some times it seems no matter how you pack it, they will find some way to destroy it. I swear some of mine were thrown on the floor, run over by a forklift, and then flew out the back of the truck in transit. I received a couple of my models back in a box of loose parts. I will say though, my last 5-6 went out and there were no issues at all, and the last 3 went coast to coast.
I went with USPS for shipping because their prices were cheaper at the time, and I never had anything damaged through them, if you can believe that!