Doctor Who: The Newbies Guide
This is the third story in Season Six. Two episodes are missing from the archives, and the DVD includes animated versions of them.
The second Doctor is short with a beatles moptop. He tends to act the part of a fool and give events a push in the right direction rather than directly taking control. He also plays the recorder.
Jamie McCrimmon is a scots piper who met the Doctor after the battle of Culluden in The Highlanders (Classic Series Season 4). He is proud of his Scottishness and wears a kilt and carries a dirk (knife).
Zoe Heriot is a scientist from the 21st Century with an eidetic memory. Her specialities are astrophysics and mathematics. She helped the Doctor and Jamie defeat Cybermen in The Wheel in Space before deciding to join them in their travels.
Recurring and Historical Characters
Alistair Gordn Lethbridge-Stewart is an army officer who helped the second Doctor, Jamie, and Victoria defeat the Great Intelligence and its Yeti servants in The Web of Fear. In that story he had the rank of Colonel.
The Cybermen originally came from the planet Mondas, a twin planet to Earth. The planet somehow left its orbit, travelling into deep space. In order to survive its people started replacing their body parts with cybernetics. Eventually they became more machine than man, removing their emotions. Now much stronger than humans they seek only to survive and convert human beings into more Cybermen
In The Tenth Planet Mondas returned to the Solar System and the Doctor helped prevent them from taking over the planet.. In The Moonbase, the Doctor, Ben, Polly, and Jamie helped defeat a Cyberman attack on a human base on the moon. In The Tomb of the Cybermen, the Doctor, Jamie, and Victoria prevented a group of Cybermen from breaking out tombs on the planet Telos. And in The Wheel in Space, the Doctor Jamie and Zoe defeated a Cyberman attack on a human space station. All of these stories appear to take place later in the timeline than this one.
The Web of Fear sets up a few aspects of this story. It introduces Lethbridge-Stewart, and in that story, the Doctor teamed up with Professor Travers (who doesn't appear here, but the Doctor does decide to try contacting him for help in the first episode).
You might also benefit from having seen some of the previous Cyberman stories. But they're hardly essential or relevant to the plot.