I highly recommend starting with the beginning of the 2005 series with the ninth doctor. The first episode was a bit boring to me, but after that it picks up. I found myself falling in love with the stories and characters. the amount of imagination that goes into the story is amazing. The doctor doesn't die, he regenerates. And when he regenerates a new actor plays the doctor. When they first introduced the tenth doctor I thought I'd hate him because he was different from the ninth. But the writing was so good I loved the tenth doctor just as much if not more than the ninth.
Another well put together fan trailer. Huzzah! or... Alonzee:
http://www.youtube.com/watch?v=IUld2qcyNpwAnd all of his regenerations (Perhaps spoilers, but not big ones. The doctor will always be replaced with a new actor after a while:
http://www.youtube.com/watch?v=uXCpY_3Sac8