My husband and I have moved about every 4 years or so, as a result I have had to get pretty comfortable in choosing new physicians.
I look based on credentials and background, i.e. where they went to medical school, residencies, fellowships, etc. and board certifications, depending on what I need. I also look at any personal statements or statements about the philosophy of the practice, as I know there are things I am just not going to be receptive to. Once I narrow it down, I determine if they take my insurance (the vast majority of places do so this doesn't usually narrow it down much, if at all). Finally, I look at how easy or difficult it is to make an appointment, I want to ensure that I can make appointments easily if needed, and don't have to wait more than a day or so for an appointment. Also, I prefer if they have an online booking tool so I can book out of normal office hours if something comes up when the office is closed.
I will happily see an NP or PA, but all of my healthcare providers right now are physicians and usually are as I have a complex medical history.