Pediatricians are truly one of our greatest resources throughout our parenting experience (and one we're paying money for!) so gather their wisdom and make your appointment last far beyond the half-hour face-to-face with their recommended reading.
If you go with a doctor in a solo practice, find out who covers when he's away. If he's part of a group practice, ask about the background of the other doctors. Some practices have pediatric nurse practitioners. They are fully trained nurses often with an MA and specialized training. Physician assistants are not nurses. They have college degrees and two years of physician assistant training.
Some offices function with phone calls and letters. Others have text messaging and email access. Neither is necessarily better or worse, but determine what would be easiest for you and your lifestyle.
Take note of their answer and research on your own if what they recommended is something you would choose too. I once had a pediatrician recommend a liquid vitamin for my six-month-old. I was shocked to find the first ingredient was high fructose corn syrup. No doubt that pediatrician and I were on different pages when it came to infant nutrition.
Some offices accommodate same-day walk-in visits. Ask how after-hours emergencies and questions are handled.
Talk to him about breastfeeding, circumcision, alternative medicine, vaccinations, sleep and discipline issues.
Please share your answers.
It's impossible for pediatricians to be experts in everything, so feel free to ask what they enjoyed the most about their medical schooling, specialized seminars they have attended and ongoing research they are a part of. One pediatrician I interviewed had extensive experience with infectious diseases in third-world countries. Another was very familiar with milk allergies and intolerances due to his own son's experience. Another saw that my daughter was wearing a cloth diaper and immediately shared that her child had the exact same one!
They may not be able to give you an exact answer due to patient privacy, but I would expect them to know a decent range with a short explanation of their vaccine policy and general philosophy.
Ideally, at least 20 minutes.