I would suggest Public Administration because it deals more with the pragmatic topics you suggested. The classics of Public Administration include a combination of political science, sociology and business/management/economics.
I agree with the statement about finding a professor you can work with first because of how important that relationship will be to you completing the degree. I also highly suggest you look into the structure of the program if you are looking to do this part time or do not plan on an academic career. PhD programs cater to different niches and design every aspect of the education towards that end goal. Not that one style is better than another, but fit matters more for a PhD then BA or Masters.
Good luck and thank you for your service.