Unless the transportation company knows you, you will be expected to pay prior to shipment. Check the classified section of a breed magazine or a regional agricultural newspaper. If the livestock involved is for future breeding stock or performance material a vet check is in order . Generally the vet will check heart and respiration, soundness in horses, eyes, ears, obvious physical discomfort, nasal or eye discharge and other specific items on request. If you are going to insure the animal, the insurance company will require a vet check for their records, so you can do both projects in one call.
Insurance is available from various companies to cover the livestock.
The price charged is a percentage of the value of the animals and you can set-up different configurations. Regular policies are for a year, but you can sometimes purchase 'trip' insurance. This is only a suggestion to the buyer, but is not a bad idea if you are shipping a long way. If you are shipping between two or more states there will be certain requirements in paperwork and vaccinations. The costs involved are the responsibility of the buyer, unless other arrangements are made.