One more thing that certainly matters: one of the main criteria in choosing a therapist is your subjective feeling. Do you feel comfortable with this therapist or not? The therapist is the main instrument in this profession, so it is important to find the person who suits you.
The method of psychotherapy also matters. Interestingly, clients who need a strict setting very often choose something without clear boundaries. Ask yourself why. Why this particular method? Every method has its own limitations and possibilities. Discuss this with your therapist.