Robin,
I think it is great that you are considering joining the military. Do you have any idea what you want to do in the military?
Someone mentioned a direct commission into the US Army Medical Corps as a Social Worker. My understanding is that that path requires a Masters in Social Work, so you might not qualify.
As far as your physical fitness goes, if you are enlisting just go for it. They will get you in shape as you go through basic training. If you are commissioning, you will need to pass height/weight and the Army Physical Fitness Test prior to joining. An officer who is overweight or out of shape will not get the choice assignments or jobs.
I would recommend changing your verbiage. You joining as a woman, who happens to be transgender, not a trans woman.
Your target gender/sex you might need to update your information prior to joining. They will need some form of documentation to establish if you are male or female. Being one of the other will change things in your service, for example APFT is sexed as are uniforms. I would think changing your legal name and gender prior to signing any contracts. This would probably include changing your Social Security info and possibly your birth certificate. Being a college graduate is a requirement for officership, so I would think your transcript needs to be updated with your female name. I would also recommend letters from counselors and MDs stating your far enough through gender transition that you should be considered female.
One of thing that stops people from commissioning is the requirement to obtain a Secret security clearance. Being LGBTQ is does not disqualify you from a clearance, but not informing the investigators could. You will most likely have to give them your dead name to complete the investigation. The big thing that stops a secret clearance is personal finances, specifically debt. People with high credit card debt are easier for agents to manipulate into selling information. If you are seeking to service that requires a clearance get your finances under control. College debt isn't such a big deal, and the Army does have college loan payback programs.
Finally, I think Rakel said something very important. Military service isn't a lifetime commitment. Most people complete their initial service obligation and move on to another chapter in their lives. If you join and it's not what you hoped, complete your tour with honor and move along.
All the Way,
Jane
