I started my transistion before I told anyone about it, as I'm sure a lot of girls here have done. And it certaintly isn't selfish to get your life in order before having to explain what Transgender is to your family.
I still live with my parents, and I came out to them just before I went full time about two and a half months ago. While they do find it difficult to deal with and have greived over the loss of their son, things are pretty much back to normal now (better in my opinion). Infact it was my birthday yesterday, and I got a card from my parents addressed to "Bee" (which was a turning point as they have never used any form of my new name as of yet). They're getting there. Considering they are past retirement age, I'm impressed how well they took it.
The only thing I regret now, is not talking to them personally when I came out. I gave them a letter, because I found it very hard and didn't know what to expect. I could have stayed with them while they read my letter and then see if they had any questions, or even read it out loud to them. Hindsight is a wonderful thing.
But, only you know your family and from that you need to judge (or guess) how well they will take such news. As I said above, give yourself the knowledge first, and then you'll have more confidence when the time does come to tell those closest to you.