Hi,
You're right, choosing a therapist is a tricky thing, and often it's a bit of a crap shoot. It's important to work with one who is a good fit for you and your needs. Sometimes that means seeing a few before you hit on the right one, sometimes you hit it off with the first one.

About your specific questions...First, the word "therapist" is rather generic. It doesn't even apply only to mental health workers. Many different clinicians and practitioners can legally call themselves "therapist". When talking about therapy, most of us refer to the person we see as our therapist (or "T"), but they could be a psychiatrist, a psychologist, a counselor, social worker, or some other type of practitioner. For the most part, among the types you mention, only a psychiatrist can prescribe medication. There are two (I believe) states where certain psychologists with specialized, extra training can prescribe, NM and LA. They are very few in number, so the majority see a physician of some kind, such as a psychiatrist for meds. A clinical psychologist is someone with a doctoral degree (PhD or PsyD) in clinical psychology and specific training in working with people with mental illnesses. They focus on psychotherapy of all kinds. It's common to see a psychologist for therapy and a psychiatrist for medication, and it's great if the two communicate about your case as needed.

Hope this helps.

gg