Doctor Who: The Newbies Guide
This is the third story of Series 3.
Other Guides to this Story
The tenth Doctor wears a brown pinstripe suit with trainers. He is much more jovial and good-humoured than his ninth incarnation, appearing to have largely recovered from the mental scars of the Time War. He does, however, have a hard edge to his personality, being the sort of man who doesn't give second chances. In Doomsday he had to leave his companion Rose Tyler in an parallel timeline, and he is still coming to terms with her loss.
Martha Jones is a medical student from 21st Century London. She encountered the Doctor when her hospital was taken to the moon in Smith and Jones. This is her first trip in the TARDIS.
Recurring and Historical Characters
The Face of Boe is an extremely long-lived being who briefly encountered the Doctor in the stories The End of the World and New Earth. He resembles a giant head in a tank.
Novice Hame is a cat-person who - alongside other members of her religious order - was involved in breeding humans for use in medical experiments. The Doctor stopped the order in New Earth.
The Macra are giant crab-like aliens. The second Doctor defeated a group of them in The Macra Terror, but the version of the species found here bear relatively few resemblances.
It's probably worth seeing the Doctor's previous visit to New Earth in New Earth, though there's very little in the plot that depends on that story. There's not much point to tracking down a reconstruction of The Macra Terror, since the Macra in the two stories have very little in common.