Good therapists are non-judgemental. Whatever you say to them is true for you. If you mention something that a therapist thinks/feels/believes may hinder you, they'll gently guide you to it and help you develop the tools to deal with it. Case in point -- my therapist detected a lack of assertiveness on my part, i.e., in certain situations with some authority figures I was either passive or agressive (or worse yet, passive-agressive,) and not assertive. He suggested I get a few books on assertiveness training, and we talked about the differences between agression and assertiveness, and anger and resentment. The effect of doing this 'homework' has been real and positive.
But, that's kind of icing on the cake. You're there for your feelings of having a mis-match between your body's gender and your brain/mind/inner gender -- what's called 'Gender Identity Dysphoria', or GID for short. Nothing you tell a therapist should surprise them, and if they specialize in gender issues they've already heard it from their other clients. Relax! Tell them about your crossdressing, about your fantasizing about having been born in the other gender, about the way you sometimes behave inappropriate to your body gender. Here's someone you can finally talk to about your 'dark secret'.
I was kind of lucky -- my mom worked in the field of mental health all her life and, although I'd never seen a mental health professional until I met with my GID therapist, I had an idea of what to expect. He asked what he could do for me, and I blurted out I wanted to become a woman -- we were off and running! WHEE!!!
As for the poor selection in your area, be a good shopper. Try them all. If you get any negative vibes, any hint of negative judgement, pay them for the visit and thank them and move on. What you told them has to remain confidential. If they blab, you have the legal grounds to sue them for big bucks (and the money will come in handy for your transition!) And there are also some telephone-based therapists. I use one, because of my work situation.
Remember, just because you're 'different' from 'normal' people doesn't mean you're not okay. Now go out and find a good therapist to help guide you on your transition journey!
Haz
EDIT: WHOOPS! That's 'Gender Identity Dysphoria', not '-Disorder' -- FYI, Dysphoria is the opposite of euphoria...