Thank you for your post.
I think you bring up a lot of familiar questions and concerns with many who enter into a new therapeutic relationship.
I have only been in therapy, with a Psychologist, consistently for one year so my experience is not as broad as many others here.
I saw two other counselors on and off for a few months at a time in the past.
I currently also have a psychiatrist I see regularly.
That being said, I agree with those who encourage you to be open and honest and put it all out there.
By this I means in terms of suicidal ideation, self-harm, medical diagnosis, even your last menstrual cycle.
In time you get to decide how much of your past and story you want to disclose.
The reason I hope you will consider disclosing where you are emotionally, mentally, etc. is the therapist needs to know if they have the skills to help you.
If you are suicidal and the therapist has no experience working and helping people through the challenges of that reality...you need someone who can...or at least a therapist who will seek support from colleagues who can guide them.
My psychiatrist asked about menstrual cycles etc. He even wanted me to have my thyroid tested right in the beginning. Truthfully, if you are a female and your menstrual cycle is irregular or your thyroid is out of wack it can cause a host of ill side effects and emotionality.
In terms of concern the T in question will bail before you get started...it is very likely, if they are any good at all, that what ever it is you have to share or say...will not surprise them or catch them off guard. They hear all sorts of things from all variety of people. For me that was one of the best things about therapy...being able to say anything and not have a therapist over react or freak out.
I hope this helps.
I hope you find a good fit with your T.
Trust the process.