How do you decide which type of mental health professional to see if you are thinking of getting help for various issues?

Consult with someone. If you speak to any professional from any of the various specialties (psychiatry, psychology, social work, counseling, etc.) he or she can explain the services available and make a recommendation for you. If you see a licensed mental health professional you will have the assurance that the individual has passed rigorous exams and is at least minimally qualified to provide services for you.
Doctor. If ypu have a family doctor you should get their advice. If not you probably should see a counselor or psychologist as psychiatry may be very hard to get in to.
Getting help. Start with your primary care physician. He or she will make the appropriate referrals..
It depends. It depends on what you are looking for. If you are looking for medication, seeing a psychiatrist is the way to go. For some forms of psychotherapy and psychological evaluations seeing a psychologist makes sense. You may want to talk to a few clinicians to see what their specialties are and which kind of therapy they practice. Insurance companies usually have specialities on file.
Many kinds. There are many different types of psychotherapy on the other hand, such as psychoanalytic, psychodynamic, cognitive behavioral, and gestalt, just to name a few. If you were seeking psychotherapy, I would suggest reading up on all of these types of psychotherapy, and choose which one sounds the best for you.