Nah, you're looking at it exactly the right way. Preparing some notes in advance will help you organise your thoughts and reduce your anxiety.
The first thing to bear in mind is that the therapist deals with gender-dysphoric people every day of their working lives, so they'll recognise the signs when they see them. All you have to do is tell them about your experiences, and they'll join the dots themselves. The purpose of the initial assessment is two-fold: a) to see whether you describe symptoms of gender dysphoria; and b) to rule out any mental illness.
They'll ask you about your current state of being (i.e. what's triggered your need to seek their help at this point in your life), and they'll ask you about your background. So to prepare for this, write down why you currently feel dysphoric and in what way (social? physical? sexual? etc.). Think about how these things make you feel emotionally, how they affect your sense of self, how they impact on your day-to-day activities.
Then write down whatever you can remember of your earlier experiences (e.g. childhood, teenage, puberty, adulthood) and how
those experiences made you feel.
The therapist is looking for persistent history of gender dysphoria. Your OP suggests that you have exactly that. So just paint the picture for the therapist, and they'll understand.
Oh, and don't worry about the fact that you've been depressed, or that you've locked up your trans* feelings for years. These are things that happen to almost all of your therapist's patients, so they won't count against you.
Good luck!