Much of the research into local availability of good-talking species can be done at home. Check newspapers, telephone directories and favorite bird magazines for breeders or dealers in your area. Call ahead to inquire about availability of chicks of the age and type you desire. Some aviaries require an appointment to see birds.
A pet parrot can be an extremely expensive, (occasionally) invasive and long-lived acquisition. Don't rush into a decision. If the dealer is local, leave your checkbook home on that first visit, and avoid a dealer who seems to be pressing for a quick sale. Dealers who care most about the quality of homes their babies go into are likely to have done a thorough and effective job all around, including crucial early socialization.
For the well-being of the birds, don't go to many stores or aviaries in one day. If possible, bathe, and change clothes and shoes between each facility. Politely observe store etiquette, which may include asking that before you handle a particular baby, you wash or disinfect your hands and step through disinfectant to minimize possible disease transmission. Don't provoke the birds by waving your fingers in their faces.
Ideally, look for a very young bird, preferably a bird that has been weaned for a month or less. If gender is important to you, ask to have the baby's gender confirmed by DNA testing. This process is minimally invasive, requiring only a drop of blood from a clipped toenail. Don't dull all the bird's toenails, however, because babies, especially baby greys, need those sharp talons to prevent phobia-inducing falls during their first klutzy year.
Look for a bird that is interactive and interested in sights and sounds. Look for a baby that expresses interest and attention by puffing out its head and neck feathers, stretching its wings (singly with a leg out or both shoulders stretched straight up), bobbing its head up and down solicitously or quickly wagging its tail from side to side. These easily observable happiness behaviors are indications that the bird is interested in what is going on. Look for a bird that responds to your voice with these behaviors, especially if the bird is so young that the feathers are not completely opened. If the bird is old enough that iris movement in contrast to the pupil of the eye is visible, look for one that frequently demonstrates excitement by narrowing the pupils. This is called "pinpointing" or "flashing," and I believe it is an important indicator that this particular bird has the interest and motivation to talk.
A new owner may feel most confident about the bird's age and socialization during hand-feeding by actually selecting a baby before it is weaned and visiting frequently, usually once a week, to handle and interact with the bird. Speech training can begin before the bird is weaned, although I prefer--for the health and safety of the bird--to have the baby weaned by experienced professionals.