For me, the only therapy that I feel is best for me is psychoanalytic because my T and I spend tons of time talking about our relationship, which echos my reasons for therapy...people problems. So I'd start by choosing psychoanalytic, CBT, etc first. I also think gender really matters. I am female and prefer a male (though he's only my first therapist so who am I to say.) My T is my age exactly which can be really weird but again, good practice for working with my peers and I agree with you age matters. Is mid-week contact important to you? If I ever choose another T I will muster the courage to ask if they would allow e-journaling because I can't do therapy well without that "e-processing" my T encourages.

Good luck on your search!