Heather-Dawn
you can watch them out of order, unless that episode happens to be part of a two part-er if you get BBC America they are replaying the older ones on Saturday nights the new season which is only 3 episodes in is on SciFi Friday nights at 9 it's a great show, try maybe seeing if you can rent the other two seasons, they should be out on DVD

Andrew A
The Empty Child/The Doctor Dances is highly recommended. It is a two part story.

practical.ambivalence
If you're interested in catching up with the "classic" series, try watching a few of the episodes starring Tom Baker. A lot of fans consider him to be the "best" Doctor (if such a thing can be said to exist), and a lot of his adventures are self-contained, so you don't need to watch an entire season. In my opinion, one of the true classics of the Baker years is "Robots of Death," which is available on DVD. And if you're interested in the Daleks, who appear in seasons 1-3 of the new series, check out "Genesis of the Daleks." As for the issue of watching the shows in order, I wouldn't worry about that. One of the things that lends Doctor Who its charm is that although the show has a certain degree of consistency from season to season, the writers and editors don't feel chained down to a single, unbending set of rules with regard to his back-story, which has changed both dramatically and subtly over the years.

mister_harold_saxon
'apparently it's a very old show' yup, the first ever episode was shown the day after President Kennedy was assasinated. Many of the original series stories are available on DVD but I assume your wanting to see the new stuff. All 3 seasons of the revamped show (2005 onwards) are available on DVD. Although there is a very subtle story arc running through each season it is not necessary to view the show in chronological order. The story arc's are more tiny hints and clues that lead up to the season finale, but you dont need to see them to enjoy the finale.