You want someone who functions as a primary care provider. Ask the person you propose to shadow if they do primary care. Some specialists do, particularly when they are just starting out and trying to build a practice.
Here's what I ask myself, "If I called this provider with symptoms of strep throat, would they have me come in for a strep test or would they send me to a different provider." (I called the office that I thought of as providing my primary care and was referred directly to an ENT for a sore throat!)