I lucked out, I had a family practitioner who was very knowledgable about Graves, in fact when I first went in for my physical and had the blood work done, he suspected Graves based on my levels. I was quite comfortable working with him, esp since he was willing to let me take the lead in my treatment. He did ask if I wanted to see an endo, but since that meant driving 100 miles one way every few weeks, I passed. I wasn’t up for that.
Family practioners are generalists, for the most part and are good when it comes to the overall health picture. However, diseases like Graves have a lot of subtle nuances and seeing an endo who is familier with Graves is a very good idea.