Hey hun,
Now, this is a very hard decision and time for you, although it is "your" body and its "your" perogative to do this transition, bear in mind, your parents may say otherwise. You need to be understanding of their position if you want to retain a good relationship with them during this. This includes; lots of talking about what problems/feelings you're facing, explaining your reasons behind starting an hrt regimen, explaining your predicted benefits from starting hrt, etc... Of course this is all hinging on the fact that they "want" to talk about it, however it seems as though your parents love you very much and are more confused and worried about feeling personally responsible for any ill results or regrets you may have in the future, if they didn't try to stop you.
I notice you prefaced your dad, now I have not known you as long as the others but, is dad a particular hurdle you foresee, or are you dealing with a single parent? Either way, you have already expressed concern over your father and chances are if you do have a single parent that much more responsibility is weighing on him.
Give him time hun, by no means am I advocating to wait on transition, data shows us the sooner you start the better your results, but put yourself in his shoes, he feels responsible for raising you and turning you into a "proper man", you saying you want to become the woman you were always supposed to be is really devastating. If at some point you feel compelled to tell him that you're taking hrt and more so to tell him why you're taking hrt, do so, that way you aren't giving him the insinuation of you asking for permission more so, you are wanting him to share in this journey of yours.

Good luck! ^_^
<3Alexis