X-Country Move/Horse Transporter - What Do I Need to Know?

We are contemplating a move from Charlotte, NC to Seattle, WA due to a job opportunity. We will have 2 horses and several other furry family members to move with us. We currently board our horses locally and will do the same in Seattle after we've visited, chosen a barn/trainer, and found a place to live. We've only trailered locally with the help of our trainer. I'll be having this conversation with our trainer but would like to have some basic information before we begin. Can you tell me what I should be aware of before choosing a transporter? Are there any precautions we can take to make sure the trip goes as smoothly and as stress free as possible? What questions should I ask before I select a transporter? Any information you can give me would be helpful. Thank you, Kris.