"Cognitive Behavioral" refers to the technique the therapist is using. They could have any kind of schooling.
I tend to be a bit of an academic snob, so I like to go for the Psychologists. But I weigh the financial cost highly in my decision too. In most cases I think your success is going to be more related to the individual's personality/style, than to their schooling.
Psychiatrists are for prescribing medications. I think they only do therapy in extreme cases. And they're Super pricey.
If you feel you know what your problem is, you could seek out someone who specializes in it, or whose studies focused on it. Likewise if you're deeply religious you might do better w/someone on the same wavelength as you (I'm assuming that's what "pastoral" means?). You also might look at the techniques they use, e.g. "cognitive behavioral" (the most common, now, as opposed to, like, psychoanalysis or biofeedback or lots of others...) . Narrowing it down this way takes a lot of research though. If you need help now, just get some.
Otherwise, your gut is your best guide.
Good Luck!!