I'd like to echo what Leah said about "being emotional isn't the same as trusting deeply." I cried at just about every session, but I did not open up very much and had a hard time trusting.

Also, I don't think it's very likely that you would make a horrible first impression by being open; if it does, run, do not walk, to the nearest exit and find a competent therapist who isn't reactionary or who minimizes your emotions.