As a current recipient of therapy, and having met with at least 12 therapists for anything from one first session to most of a year, I can say that the #1 most important criterion for selecting a therapist is that you feel a strong personal connection to him/her. If you respect, like, feel comfortable around, and bond with your therapist, you will be able to share your genuine feelings and trust what they say. This is not to say that he/she should be the sort of person you would choose for a friend, but that you feel good about going to appointments and are able to get real work done during the session.
Trust your gut! In the same way that you get a certain feeling about a person when you meet someone for the first time, you can generally tell pretty quickly how well you will be able to work with a certain therapist.
That said, don't stick around with anyone who still takes that Freudian bull$#!& seriously. I currently see a psychologist who specializes in experiential therapy and psychodrama, which I love because it's centered around physical movement, role-switching, and other more tangible ways of processing feelings than just sitting on a couch (e.g., engaging in a dialogue with your AV/better future self). As others have said, ACT (acceptance and commitment therapy, also research-proven to be effective), CBT, DBT, etc. are your best bets. And again, the approach that makes sense and feels good to you is the best one to stick with.