Your first visit they may at the most take enough blood to run some tests. Don't be too disappointed if you don't get any scripts that day. I actually had to wait another few weeks after my first appointment to even get blood drawn, then two weeks after that to get my first scripts. Not saying this will be your same experience, but that is how the clinic I went to operates. Hopefully they will draw blood during your first visit so they can get the tests done and pull you back in soon thereafter to look at the results and possibly give you your first scripts.
But definitely congrats on acquiring the HRT letter! You'll be on it soon.