So tough making us choose one! I chose emotional stability because I know T1 hurt me because that is something he lacked. I chose current T primarily due to his stability (I didn't find him particularly warm at first).
My other response (which I'm slightly ashamed of for some reason) is intellectual acumen. I need a therapist who is highly intelligent. One of my reasons for discounting the supervisor I recently saw was that she didn't seem particularly intelligent. I guess I feel like I don't want to come across as an intellectual snob, but I need somebody with an inquiring mind who can quickly understand philosophical concepts. It's not something I need in other relationships, but in a therapist definitely.