Hi, Liz, and welcome!
First of all, it *is* a very good idea to do a little research before applying for a medical! In fact, depending on how complicated your medical situation is -- if you have any doubts at all about whether the process will go smooth or not -- consider meeting with a AME (Aviation Medical Examiner) for a "consult", just to chat -- informally, without submitting any paperwork to the FAA. That person can help make sure all your ducks are in a row *before* clicking "Submit" on any forms.
Being trans will not concern the FAA. They can be persnickety about name changes -- they want your name (and gender) to be identical across your pilot's license and your medical, for instance.
Medically speaking, the FAA cares the most about:
1) Cardiac stuff -- they don't want you having a heart attack in the air
2) Neurological stuff -- they don't want you having a seizure in the air
3) Mental health stuff, like autism/ADHD/depression/anxiety
3) Drug and alcohol stuff, DUI's and other things that might indicate abuse.
If you do a little searching through the threads here in the "Medical topics" forum, you'll see that when people get tripped it's by one of these four gotchas. Like an SSRI that they got prescribed once, or a diagnosis of "anxiety" from the past.
All this being said, there is also a flying option that does not require a medical certificate at all: it's called "Sport Pilot". It allows you to fly FUN little two-seat planes during the daytime. Some find it a way to "get started" in aviation, while others just have fun with it and never look back.
Edit: yeah, same as what DaleB said.