A question about gender identity and sexual orientation

I recently decided that I'm transgender. After struggling with my identity, i've decided I don't identify with the gender I was born as. I'm having trouble coming out though. I live near Scranton, but I'm not sure how everyone I know will take it. My parents are both conservative, though my dad more so. My dad whines about "liberal bias" in trying to promote tolerance of sexual minorites, so he probably wouldn't take kindly to me coming out. My mom doesn't see anything wrong with sexual minorites, but she believes that being "anti-gay" doesn't make you a bigot. My dad has said such things as "If there is institutional racism, it's institutional racism against whites," and "Most of Congress are men because women aren't as interested in politics." Most of my friends are the brogressive, Louis C.K. worshipping types, so they might not accept me either. However, I was wondering, is there any relation between sexual orientation and gender identity? part of the reason I object to "LGBT" is because I believe gender identity and sexual orientation are seperate. Correct me if I'm wrong, but since I am attracted to women, I am a lesbian? I'd guess that I am a gay trans women, but are the two related? again, I'm not sure of this, so please correct me if I'm wrong.