Your list would probably be mine down to the last word. But finding someone to meet all those criteria - not easy.

My attachment and abandonment issues are the biggest for me. I need to know my T cares and is available (Mine's not THAT available, but I understand she has a career, a life and other patients too)
It took me a long time to be brave enough to ask her if she really cared, adnd once that was confirmed, it made me feel much better, but also made the attachment issues worse...
For me, I don't know if I could connect with a male T, so I needed to find a female T.
I also am not very good at being the first to talk, so I like the fact that my T is prepared to get the conversation started when she realises I need a kick start.
I am an arguementative person and like to analyse things too - I needed a T that was prepared to challenge my thinking, and make me look at things from different angles (She is not afraid to tell me what her personal view is on something) (She has a very much psychoanalytical approach to therapy)

Well, those are my 2 cents worth