Hard carriers can be very useful when transporting cats by car. They are generally made from sturdy plastic and have a metal grated door on the front so the cat can see out. Air holes line the sides as well to let light in and allow plenty of air flow. Hard carriers are available at almost any pet store.
To make the crate more comfortable for your cat, get him used to it on his own terms first, if possible. Leave the crate open on the floor of your home with a blanket inside for comfort, along with some toys and a few treats. Let your cat go in and out as he chooses and make it as pleasant as possible for him. A crate can accommodate two cats if they are smaller and comfortable with each other. Otherwise, you will need one crate per cat for travel.
If your cat is restless during transport, cover the crate with a towel to prevent the cat from seeing out. It can calm him and encourage him to lie down and go to sleep for the remainder of the trip.
Soft carriers are recommended for air travel. They are smaller than hard carriers and can be brought on board the plane as a carry-on. Most hard carriers are larger and would not meet carry-on requirements for air travel. Soft carriers are made of fabric and leather and some have tethers that help keep your cat secure inside. Many varieties have net meshing that let the cat see out and provide ventilation, like the air holes in a hard carrier. Many soft carriers open from the top like a purse so the cat is not likely to jump into one of her own choice. However, use of bedding can make the soft carrier every bit as comfortable as a hard carrier and most cats won't mind the smaller space.
These carriers are also conveniently stored and can be folded into a suitcase or closet when not in use.
Some people prefer to use the services of a pet shipping company for cross-country moves or if they are traveling internationally. The company provides all the shipping services, including the containers, and keeps your cat comfortable during transit. They also assist with any legalities involving importing pets to a new country. This choice is best for longer or more strenuous moves or for international transit.