Oh man. Personally, I think it's unfair that just when things feel hardest and we're finally interested in talking to someone, it's usually exactly the time when we have the least capacity for dealing with it. But, it's not actually that hard, just takes some time. Below are some thoughts based on my experience in a large city with lots of therapists -- I know it can be quite different in smaller towns.
Most therapists will offer a free short phone consultation - they can hear a bit about your situation and you can get a sense for their personality and overall approach. It's sort of like a first date - you don't have a lot to go on but you can usually get a sense of whether you'll get along with the person.
If you have one, or a few, or even dozens of sessions with a therapist and decide they're not the right one for you, then you can find a new one. It happens all the time. Don't feel obliged to keep working with someone. It's professional -- just let your therapist know it's not working for you, and move on. And your insurance won't care that you're changing therapists.
Considerations:
1. Your insurance might prefer an in-network provider, so that might help you focus on a smaller set of options. Reimbursements for out-of-network therapists don't necessarily cover very much of the cost. In my area, very few therapists are affiliated with insurance, so I've had to pay quite a lot out of pocket to get a good one.
2. Many therapists don't have time slots for new clients, so it can take a lot of calling / emailing to find one. It's worth sending out a bunch of queries at once. I wrote a standard email and sent it to a handful of therapists who looked reasonable. I used a similar script for voicemail. Something like:
"Hi, I'm Grayscale. I'm looking for a therapist and your name came up as a good option [mention if you were referred by another provider who knows them]. I'm X years old, I work in [career], and I have been struggling with [quick synopsis of your broad concern]. If you are taking new clients, could you please contact me at [number] or by email at [address]?"
3. Modalities / specialties: There are a few choices -- you might not know what you prefer, and that's ok. This is why you might have to meet with a few therapists to find one that works for you. It's really more about clicking with the person than something you can discern from a list of skills.
* Some therapists list specialties (eg, LGBT issues, or ADHD) but most are pretty broadly trained to work with many types of patient and many standard concerns.
* Modality: the big divide here is Cognitive Behavioral Therapy vs more classic talk therapy. CBT is very popular, and proven very effective for concerns like clinical anxiety, depression, and PTSD. It uses a lot of worksheets. Classic talk therapy (I'm sure there's a technical name) is more like having someone listening to your concerns and helping you untangle your thoughts and your history. It's also very useful. There are other options, and most therapists use a combination of these.
* PhD psychologist vs master's level MFT/LCSW vs MD psychiatrist: Psychiatrists are overkill for most concerns. I used to prefer people with PhDs because they could relate to my own career path, but I've realized it doesn't actually make a difference, and I've had better luck with MFT/LCSW (MFT is marriage and family therapy but they often do individual therapy also).
psychologytoday.com is a commercial site but it does have a pretty large directory of therapists, with info about their approach, specialties, availability, and insurance.