Mine is a psychologist. I did choose him in part because of his level of training but not entirely. I had it narrowed to two in my town (same office actually). One was an LPC and mine was a PhD. I went with the PhD. Worked out since the other guy ended up moving away a few months later.

Insurance coverage was my first criteria for choosing a therapist. There was no way I would have been able to afford therapy without insurance, so I worked from our insurance list and narrowed it from there.

I've had three different therapists, all very good, with three different training and degree backgrounds, so I don't put a huge amount of weight on titles. Quality is quality.