Hi Moni,
I would try to find any trans resources in your area that may provide a guide for various resources and processes (including name/gender change requirements for your state). As these requirements are different for different areas, you may stumble upon exactly what is needed based on experience.
Is there a reason you want/need to get the gender change done by a certain date?
If you already had your court appearance and court order for your name change, I might suggest working your way through Social Security and MVD. I have found that besides insurance, Social Security, and MVD there are not many places where your gender marker comes into play in day to day situations. Heck even when I get carded, I've never had any issues in regards to gender marker.
If there is a hard deadline it may also be worth getting as much of the name change administrative paperwork out of the way, making the gender marker more of an amendment to whats already completed.
If it is the amount of actual prep/face time with different organizations, having a full set of documents with you can be handy. I have lost count of the number of times I happen to have an extra 30 min, AND am right next to a place that needs updating.
In any case I wish you luck and ease in the legal paperwork.
Brooke