I think you need to understand that in general very few therapists will prescribe HRT on the first visit. To do so rides a coach and horses all over the WPATH standards of care documents which I believe require that you have been in therapy for your gender issue for at least 3 months before starting.
I do know of a FEW people who have managed it, but they are rare, and in general I would observe that people who seem to be in too much of a hurry tend to make therapists nervous. You see they worry that if you do something in a rush, you may regret it just as quickly.
So I have to say that I think you will just have to do what pretty well all of us do and play a waiting game.
There are a FEW therapists who will prescribe HRT on the basis of informed consent. If yours is one of them then you may be in luck, but if not then there is not much you can do.
As regards how to play it, the only answer I can give is "Be honest!" This is your life we are talking about and the only way to get a good result form therapy is honesty. Sure you can tell the therapist what you want, but you also have to be prepared to answer their questions truthfully, and to work with them, rather than demanding things which they may not be willing to give.