This seems to vary from place to place. Where I am the therapist is a psychiatrist with an interest in gender issues. In the USA it seems to be all sorts of things.
The gender of the therapist makes no difference to therapy, it is purely your preference. My initial therapist was male, he was great. My current therapist is female, she is great as well. Then again they are professionals in their field.
What do you need therapy for? Be careful here. The role of the therapist is to help you. If you have issues that need dealing with they need to help you deal with them.
If you have a psychiatric co-morbidity they need to help with that. It is often overlooked but the suicide rate in post SRS MtF is essentially the same as in pre, that implies there are is a significant group of gender dysphoric people who need help dealing with their lives beyond straight gender issues.
I had and have no issues, I needed letters to change name, gender ID etc on legal documents and of course to access HRT and surgery.
Good therapy is something to help you, not to hinder you.
Make sure they have experience with gender dysphoria, that they are aware of the WPATH standards of care. They are qualified to treat and refer you.
On meeting them that you are comfortable with them, yes you will be nervous.
A good therapist can probably be picked by an opening statement from them. Along the lines of: "Hello, what name would you like me to call you? I do not care how you present for our meetings as far as presentation clothing is concerned. Please dress in whatever clothing you are comfortable to present publicly in"
After a session ask yourself if YOU are comfortable. You may feel confronted, but are YOU comfortable.
What are your expectations, set the boundaries that you want, ASK.
Where I am for an adult it will take a total of one hour and forty five minutes to be recommended for HRT if there are no issues to be dealt with. One 45min and two 30 min discussions. This may of course take several weeks to get the appointments, so in practice it is about 3 months.
Where I am (South Australia) I have to keep seeing a psychiatrist by law until after I have surgery. I see her for 20 mins every 3 months. Last time we talked about Game of Thrones, this time probably the finale of Breaking Bad. I have nothing to be treated for and she knows it, we have meetings to cover the law so I can have surgery.