In my situation, I started by making an appointment with the Diversity person. She set up a meeting with my boss, and she handled telling the department head and VP-types. I only had to directly come out to my boss and immediate co-workers with the Diversity people present.
Gender identity was a recent inclusion in the policy at my workplace as well, and it really took some of the stress off me knowing it was there.
When I met with the Diversity person, I came with a list of concerns and solutions - and she took copious notes during our meeting. Be prepared to answer their questions and provide a list of people that need to be informed, when you want to come out, which bathroom you intend to use, when you're applying for your legal name change, etc. Having all your ducks in a row going in will make you appear confident and prepared and capable of transitioning so as to cause the least amount of disruption.
If you're already presenting male, which I was, too, you should be fine. The only new thing I added after coming out was men's shoes 😛
-Jay