When I had a great internist I went to her first. She was a great diagnostician and great at getting me into specialists. She closed her individual practice and now works for the local university in student health. I’m now on the 2nd replacement and while she is very nice I’m not sure how helpful she will be. She works for a large health network in a larger area that is making inroads in my community.
I have a dermatologist, orthopedist, gynecologist and urologist and physical therapist that I call to make direct appointments with. For things that come up as @abasket mentioned I go to the urgent care run by the hospital. @ucbalumnus question I do not update my internist. The place I do labwork sends results to both the specialist and the internist.