I wouldn't ever, EVER use "Boys Don't Cry" to educate family....aside from the blatant lawlessness/sex that the community shows, the violence shown toward Brandon would scare my family sh**less and cause them to want to "convert me to normal" as if they were saving my life. Some of my family would also twist and misconstrue it to "I want to be a boy so I can get into straight girls' pants easier" or some bull like that.
I've honestly seen very little TV that I felt was a comfortable representation of a transperson. The worst being of course Jerry Springer episodes (which are pry the reason why I have had so much issue coming to grasp with the idea that I am not a sideshow freak).
The best I've personally come across was an episode of Dead Like Me, where Daisy Adare goes to a plastic surgery clinic to collect a soul. She assumes it to be one of the two snobbish rich women in the room, but the soul ends up being a very normal-looking, if not timid, man in the corner. When she finds the name matches her post-it note, she replies "I thought you'd be a woman", to which the timid-looking man replies with a smile, "I will be soon." One lethal high heel to the forehead later, they both have a conversation (the transwoman now dead, and just a soul) and the story arc ends with them making one last trip to a church, where she wished to visit before departing. She starts throwing things at the altar, breaking down in tears and asking aloud why she was born in a male body in a pretty powerful scene. I liked the story arc simply for the ending, as there were things I didn't like about it...but it didn't pose the transwoman as a drag queen or in a poor light, Daisy remained supportive through the conversation and they talked about things like it was nothing at all odd, and the end outburst was a monologue of the discomfort and confusion we all feel about the bodies we were born in.
That said, I don't watch TV much. That one episode wasn't really fantastic for outlining any really big steps forward in daily life of a transperson, but did show me one of the first real positive images I got from TV about transpeople.
Teknoir has a very good point about the "phase" issue. If you do, I would also suggest staying away from anything that treats transpeople in a violent manner, as I stated before...your family could attempt to put you on lockdown to "protect you from yourself".
