With the right skirt or dress, tucking may not be much of an issue, but I used to wear men's Medium underwear and now I tuck things away with a combination of XS women's thongs and Small panties since I usually wear pants/shorts instead of skirts/dresses.
When you are comfortable with changing your name and feel you can or want to present as female everyday, then you can go ahead and change your name and gender markers on your IDs at that time. Otherwise, you suffer until you can make the documentation changes. Some states require SRS before changing a birth certificate, but most other documents can be changed without that.