The use of the word "type" usually refers to the degree a therapist holds, i.e., M.A., M.S., Ph.D., Psy.D., or M.D. First of all, it's important to separate two main elements: degree attained versus license held.
License held refers to an individual who has already completed a degree of one sort or another and has passed additional tests, usually administered by a state licensing board. These tests may be written, oral, or both. To date, they are the only measures of competency available, and for all their ills are probably better than nothing.
Degree held refers to the education a therapist or counselor has received prior to being licensed. However, don't be misled by this last statement: Just because someone holds himself or herself out as a therapist does not mean that he or she is licensed! Basically, degrees are often described as being "medical" or "non-medical." This simply means that unless one holds an M.D. (that is, a Medical Doctor's medical degree), then the degree held is a non-medical degree. This is an important distinction because an M.D. is qualified to prescribe and administer medications, and none of the other degrees permit such practice.
There are other distinctions which may be important when deciding which type of therapist to see, and those are covered in the "Who Are These People?" FAQ. Otherwise, the type of therapist you wish to see will be somewhat dictated by whether or not you have a sense of whether you want or need medication or an evaluation for medication, or whether you strictly want psychotherapy. If you are not sure, any competent therapist can help you determine which is appropriate.