“When shopping around for an advisor, the idea is to fit the type of advisor and stages of their career development with the personality type and goals of the prospective student or postdoctoral fellow.”
This excerpt is from an article on the science careers website of the Science Magazine of AAAS. (http://sciencecareers.sciencemag.org/career_development/previous_issues/articles/1820/choosing_a_graduate_or_postdoc_advisor/)
While you can read this long article which pretty much covers every aspect of the topic, I want to emphasize how important that you get along with your future advisor. Getting along with your advisor will make things a lot easier and your graduate life much more enjoyable. Some of them are more hands-on and spend considerable amounts of time in the lab with the students, while others are very busy with administrative or teaching obligations; some are more laid-back nourishing, while others like to be in control and push hard. There is no one best style for everyone but you can figure what fits you best. You can learn about the culture of the research group by talking with the group members. Inquire how the professor would like to receive information. In some group you present at a lab meeting every month while in others you might only need to present once every semester. If you plan to have children during graduate school you will want to make sure the pace and stress levels in the group would allow you to do so. You will find in some groups rules and policies are set for expectations in terms of hom much vacation time of a year you can have and how many publications you need to produce in order to graduate. These are some of the things you want to know before joining a group. I’ll let you read the Science article now.