Most psychiatrists deal with anxiety and depression. So you don't need one that specializes in say, eating disorders or trauma, etc. (as far as you've said). That's good because you have a lot of choices, but bad because you'll might have to search a bit for someone you really like. Make an appointment, factor in if you care if it's a male or female (or any other preference), and use the first visit to explain what you need and ask him/her questions and see if you like the approach. Then go home, don't make another appointment right away unless you are totally sure you like the person. The psychiatrist may even tell you to think about it... both my psychiatrist and therapist told me to call them if I wanted another appointment and didn't press to get a followup right away. That's how it should be in my opinion. Give it a day or two to settle... and if you don't think it'll work with the first one, make another appointment with someone else, and repeat. If it's a solo or small practice, you may be able to get a few questions done over the phone.
Personally, and this is just my preference, I like going to doctors that are in their own office or that at least have about three doctors/therapists or less. I feel like I'm just a diagnosis if it's in and out, one after the other. But that's just me. It took me a while to find a therapist I liked, I think I went to five or six people before I found the one I liked. I also had a therapist before this, and she was good for what I needed when I was really suicidal and needed to go inpatient for trauma treatment. She got me there, and through the month or so before I could go. I was self harming, but I made it. But when I learned a lot inpatient, I realized she wouldn't be any good anymore for what I was going to need to talk about. Doing something like saying "hey, it's not working out" is really hard for me to do, but it was important and she was very nice about it and I think she kind of realized I needed someone else, anyway. My therapist suggested the psychiatrist I go to, and he is perfect for what I need.
Sorry for the long post. Good luck with finding a doc.