This is a little old but hopefully you'll still see my response:
It depends what you're looking for. An emotional support animal can be chosen just like any other pet - find one that suits your needs, from a shelter, rescue, breeder, etc. They are essentially just your pet, but since you have a diagnosis and a pet will help you cope, you can do things like bring them on planes, have them in no-pet housing, and bring them to hotels.
A task trained dog is a dog that will perform tasks at home, such as waking you from hypersomnia, tactile stimulation to prevent dissociating/flashbacks, fetching medication, etc. Many regular pets can be trained to do this, but it's best to seek out a dog that has traits like biddability and will be unlikely to form anxiety from your condition. Any trainer can help you choose a dog for this from a shelter and teach them the tasks, and a breeder can help pick a puppy best suited for it. This dog can be a registered ESA, or just a regular pet trained in tasks.
For a service dog which will be able to accompany you in public anywhere you go, you will need to pick a dog that has been carefully evaluated. Many working services dogs come from shelters, but it's hard to choose without a lot of experience, and with shelter puppies you don't know what their adult temperament will be. If you're looking for a puppy and not an adult, a breeder who has had dogs go on to service work before is the best bet. If you're willing to get an adult dog to train, a trainer can help you evaluate a shelter dog (preferably one in foster care) or pick an adult dog from a breeder.
Since you asked about specific breeds, common service dogs are labs/goldens/standard poodles/mixes of those breeds, but any breed can work as a service dog. It will depend on specific tasks you want and what will fit into your life. If you need a dog to do guide work or make you feel protected and you're tall, you'll need a large dog. If you want a dog that can sit on your lap in a restaurant for stimulation, a smaller breed will be better.
Good luck! There is a lot of service dog info here if you search around