I can only share my own experience, so please don't take my own as a sign of what it will be like for you.
On my first appointment, I was basically asked simple questions by the Endo. My therapist had faxed over a letter, but she didn't recieve it. Therefore, my endo was a bit more cautious with me and really made sure this is what I wanted. She told me that there are risks and there is no going back, so she wanted me to 100 percent comitt then and there. After that, she gave me a script for blood work and told me that she will look over that, as well as my therapists letter and then will start me on hormones depending on how it went. It wasn't bad at all. She just wanted to make sure I realized what I was in for and she wanted to verify that she was working with someone that had their entire heart set out for it. She could have been gatekeeperish with a different patient, but she was easy going enough and sympathetic.
I dressed the way I usually do and don't remember her looking at my genitals. She does listen to my heart beat and lungs, checks blood pressure, feels around my throat, checks for breast lumps, and looks for signs of dvt on my legs. She doesn't use any needles, as I go to an outside lab for blood work and use oral hrt.
Usually, the first appointment is just an introduction, then they send you to get lab work and then only after they assess everything and clear you wil they give you hormones. That should happen on your second appointment, at least that's how it went for me.
