This may be the most important step in having a successful program. You must have a dog that loves being in the middle of large groups of kids and the kids must respond positively to the dog. There are several other key characteristics that include obedience, ease of training, size, age, health, adaptability to change, breed and plain ol' character.
When I selected Copper, it was because he was a golden retriever and local. I selected a golden retriever because the HABIC dog that initiated my interest in this area was a golden. My insight ended there. I just got extremely lucky to go through all the training and happen to have a dog that loves to have crossing guard duty on cold winter mornings and going for walks with kids down school hallways.
When Copper gets older and/or I consider getting another dog. I will put much more thought and resources into this decision. Here are some considerations:
Rescue or breeder? This is a tough decision. There are positives and negatives to each side. I've met numerous professionals who have rescue dogs that are amazing. One strong benefit is the connection that kids may make to the dog's history. An area of weakness may be unknown fears or behaviors that may not be overcome and result in not passing the therapy dog testing requirements. There are several rescue organizations that will notify professionals if they come across a dog that may be ideal for therapy work.
If you do get your dog through a reputable breeder then you have the life history of that dog. You know what traits that the breeder likes to see in their dogs and can interact with the parents. You may also have insight into future health issues.
Size - I work at an elementary school. The hallways can get crowded at times. By having a larger dog, Copper is 80 pounds, I don't worry about him being stepped on. However, having a large dog can increase the risk of injuries to young students. If I allowed Copper to play soccer at recess, a student would get hurt. During his play times with other dogs, I have to be careful. He is not great at always looking where he is going and has been known to knock adults off their feet.
A small dog may increase risk of harm to the dog by the students by either being dropped or stepped on.
Age/Health - I place these two together because they can be interrelated. Once a dog starts having health issues, they should be placed on leave until they recuperate. If they are getting older and are developing health issues they should be retired. Retirement can be gradual; cutting back hours worked, the type of client and the type of activity.
Organizations typically require a dog must be 2 years old to be certified. Getting a puppy gives you plenty of time for socialization and training before starting to work for several years. The work time is cut significantly if you adopt a dog who is 6 years old. After training, they will have a limit time to work before retiring.