Pick a therapist. Tell them you're shopping, you'd like both a trial session and recommendations for alternatives. If they're not willing to do that, they're not the right person. Most are.
A few years ago, I had decided on my own that I needed medication; the depression was so overwhelming that I felt like the problem had to be chemical, and no "touchy-feely" talking therapy could possibly help. I went to a few psychiatrists, with varying degrees of success (I caught one reading side effects of a medication off of wikipedia) and stopped going several times because I felt like it wasnt helping. It was only when things got bad that I found a therapist (I think I just googled "therapist <my neighborhood>") -- who I liked -- and she convinced me to just give her way a try. It worked.
I am on medication again, and its helping, but it was really the therapy that I was so against thats making the biggest difference. All of this is to say that find someone you like, and then be open. Deciding how you want to be treated from the outset doesn't necessarily make sense. Mental health issues are like any other illness -- we go to doctors for their advice and expertise. But you need to go.
I'm really not kidding. The range of usefulness of therapists is so large that "any therapist is a good starting point" usually works. It's better when you can ask friends, but if you can't, any therapist will do.
Then go for a brief session with each of them. You should pick the person you feel most comfortable talking to EASILY. This person should be someone you don't feel judged or threatened by. You should be able to understand them clearly and they you.
Think about it like it's a date. In a way, it kinda is.
But outside of "pick one and start there", what would you recommend if somebody can't get a recommendation from friends/family? How do you find a decent practitioner?