This depends on a number of factors, and your GP will guide you.
In a nutshell, we treat depression according to its severity:
Mild – usually support and advice, wait and see, and address the 5 key factors for good mental health – sleep, exercise, nutrition (including caffeine, alcohol), relationships and stress levels. Mild depression usually gets better without specialist help.
Moderate – either psychological help or medications (you choose)
Severe (usually means suicidal ideas) – usually we recommended all of the above. Plus we think about hospital admission.
If you’ve been told therapy – yes, you have a choice of a psychiatrist of psychologist. Both are highly trained. Psychiatrists are trained as doctors, then specialise in psychiatry. So they can prescribe medications and do therapy. Psychologist (in Australia) don’t prescribe, but they have longer training in the therapies, and so some would argue they are more skilled in the area (at least at the time of qualification, some psychiatrists only do therapy so quickly gain the experience and skills needed).
Which you choose probably depends more on who your GP works with and recommends, and which you can get an appointment with. In the long run, I don’t think it matters much, the main thing is that you give therapy a try, with someone. And you have to give it a decent try – you can’t judge it in a few sessions.
Also, it depends a little on who you ‘click’ with – make a phone call first and chat to the therapist to see if they sound reasonable. And I tend to prefer people with more experience.
One more thing – the costs are different – so ask before you book in.
In my own practice, when I have to refer someone for therapy for moderate depression (I work in a hospital and so mostly refer outside for therapy), I tend to let the patient decide and give them options for each – but they mostly end up choosing the psychologists as they are easier to get into, a bit cheaper, and often more experienced in specific forms of depression psychotherapy.
If I was choosing for myself, I’d probably choose a psychologist as my first option, but it is a line ball and there is no correct single answer.
(Note – there are also social workers very skilled in therapy of various types with training in specific therapies. I consider well trained social workers as the same as psychologists and psychiatrists when it comes to therapy, so consider them too).
At the end of the day, ask your GP, try to find someone you like and trust, and give it a go. If it doesn’t work out, go back to your GP and try someone else or consider other options.