There is no one "treatment of choice" for psychotherapy. No therapist can possibly be familiar with every effective treatment, and he or she must be open to your exploring options other than the ones he or she offers. He or she must also be open to learning from you.
While it's inappropriate and unethical for therapists to tell you the details of their personal struggles, it is perfectly reasonable to ask what particular forms of therapy they have been trained in, where they learned their skills, and whether they've personally benefited from the therapy they propose for you.
Even more important than the specifics of the therapist's training, is the relationship between the two of you. Do you feel basically comfortable with this therapist? Does he or she seem to feel comfortable in his or her own skin and with you as a fellow human being? Feeling safe is a necessary condition for you to confront your fears and anxieties. In my experience, clients' symptoms improve more quickly if both parties develop positive feelings and respect for one other. I also don't think that you can grow and change unless you feel that you have some impact on the person who is treating you.
The relationship begins before the first session. It starts with the time you spend on his or her website. Does it strike a chord with you or is it generic mumbo jumbo? Do you feel a sense of hope, believe this person can help you? Does he or she get back to you quickly when you call? Is this person's style more friendly and casual or professional and clinical? What do you prefer? Is there a willingness to be flexible with schedule or fees? How does your gut feel? What kind of energy does this person have? Do you think you might be able to spend hours sitting with him or her, expressing distressing thoughts and allowing yourself to be vulnerable?
The critical question is this: Do you feel that your therapist is curious to find out who you are and what you need? Are you just a list of symptoms on some questionnaire, or does your therapist take the time to find out why you do what you do and think what you think. Therapy is a collaborative process - a mutual exploration of your self. The therapist can provide illumination, new perspectives, practical resources, but ultimately you are the expert of your own life.