At the outset, I'd suggest reading the WPATH Standards of Care. Most doctors practicing in any area touching transgender healthcare will be utilizing the WPATH 7 standards (though some may cling to 6). You can find the PDF of 7 for free online at the WPATH website. Current standards don't set a requirement for a therapist's diagnosis of Gender Dysphoria, but most Endo's and GP's that prescribe HRT are going to want a therapist to see you first. It's a good idea in any case, because a good therapist can help prepare you for the mental, emotional, and social changes that are going to take place in your life.
I'm not even close to any of the surgeries yet, so I'm not as up on their requirements, but there are standards guiding those in the WPATH as well.
Oh, and you're not likely to find any legal standards guiding the medical aspects of transition. The legal aspects will be governed, but the medical community is generally going to control their own standards, and the law just expects adherence to those.