Get the best expert available

The basic principle is simple. In an ideal case, the tutor is the best expert who is reasonably speaking available, and has a lot of experience in tutoring doctoral work, preferably in the form of having successfully tutored several students through the process, and having examined several others.

If there is no such person available, the next best choice is to go for experience. A late colleague of mine from the University of Helsinki once noted to one of his students that he does not understand anything about the topic, but he understands what a Ph.D. thesis is, and knows one when he sees one. This works, as long as the tutor has a some degree of knowledge of the topic. Few historians can supervise work in chemistry.