I've been reading many of your posts lately, and what I'm going to respond to this post with I assure you is not meant to be offensive. Your posts contain the same questions asked over and over, and people respond over and over telling you their answers, yet the answers do not seem to satisfy you, as the question is asked again in future posts. I will answer your questions this time as well as I can, so please read thoroughly.
First of all, congratulations on having your parents support your transition, that's awesome. As for finding a therapist, if you have a local LGBT Center, they could possibly recommend a therapist to you. You need to be sure the therapist you see deals with gender issues specifically; do not see a general therapist as they will more than likely try to "fix" you before helping you. If you do not have a local LGBT Center, perhaps search the internet for gender therapists in your city/state. As for the cost of the therapist, that is something you'll need to ask the therapist you wish to see. For reference, however, my therapist charged $60 per 50 minute session.
As for changing your name; if you are under the age of 18, you will need your parents consent to change your name legally. Each state has different requirements for legally changing a name, so you'll need to review your specific state laws to see what all is involved and required. I cannot say whether you could have a legal name change by time you are a senior (re-read this paragraph as for the reasoning).
The good things and bad things about transitioning? That's specific to each person. For some, friends and family members are lost. For some, the social side of it (passing) causes further/less dysphoria and concerns. For some, physical side affects from HRT cause issues. For some, none of the above happen/concern them and they're just fine. My point is, we all are different in our transitions; as far as my opinion goes, no two transitions are the same. Everyone feels differently, reacts differently and looks differently. Overall, however, I feel we can all agree that the best thing and the main focus of transition is that it is a good thing because it calms our dysphoria and allows us to be our true self.
As for getting arrested for a DUI and which cell you'd be in, is that something you really have to worry yourself with? Don't drink and drive, obey the law, use common sense and I promise you which cell you'll end up in won't be an issue. I will not dignify any further response to this question. I cannot comment on whether the U.S. military will or will not accept you as I do not know. I'll leave this question for someone who knows a bit more.
I hope my response has helped you in some way. You seem to be wanting to cram this transition into a little ball and swallow it all at once, and that just isn't how it works. You need to slow down and take one step at a time. Your goal right now is simply to find a therapist, do not worry about anything else. Congratulations and stay in touch on the forum with how things turn out. And just as a side note from me and from what others have told you, you are very fortunate to be beginning as young as you are and you already pass 100% in my opinion.