Depends on what you're looking for. (Helpful, huh?)
I started with counselor. Because I didn't need a psychologist to explain to me what was wrong with me; I needed tools to go with my Al-Anon tools to handle my everyday life.
If I had known then what I know now, I would have looked for a counselor specializing in addictions who has a working knowledge of Dialectical Behavioral Therapy, DBT. That basically means working with radical acceptance: Instead of saying "But I love him when he's NOT drinking" it taught me to say "I loved my husband and he was abusive" without my brain freaking out about the cognitive dissonance. I've learned to hold two contradictory thoughts/feelings and look at them to find out which one comes from "my wise mind" and which one is unhealthy.
Psychiatrist is only necessary if you think you have an underlying personality disorder or serious mental illness, in my mind. Depression/anxiety, most GPs can prescribe drugs for -- although psychiatrists ARE better at knowing what drug works for what. And twice as expensive as a GP.