Being a "modern" fan of Doctor Who can be a frustrating experience. I was born between The Ribos Operation and The Pirate Planet, already three doctors down, and I never discovered the series until it was in its new incarnation. Since then, I've tried to gobble up what Doctor Who content I could, but it's a frustrating experience. While most of the series has been released on VHS, these are too difficult to find and to damaged by time to be of much use. And the DVD releases, as wonderful and as well-done as they are, are horribly incomplete. Worse, they are released in random order, perhaps as a "Best Of" for fans first, but almostly inaccessible to a viewer coming to the series for the first time.
For my own use, but perhaps for someone else's, this page gives you and idea of how much of each character's arcs are currently available on DVD. I ignore the fact that some of the First and Second Doctors' stories are lost forever, but perhaps they will eventually be released animated as The Invasion was.
The Doctors:
First Doctor - 134 episodes, 43 on DVD - 32%
Second Doctor - 119 episodes, 35 on DVD - 29%
Third Doctor - 128 episodes, 46 on DVD - 36%
Fourth Doctor - 178 episodes, 102 on DVD - 57%
Fifth Doctor - 69 episodes, 39 on DVD - 57%
Sixth Doctor - 31 episodes, 25 on DVD - 81%
Seventh Doctor - 42 episodes, 18 on DVD - 43%
Eighth Doctor - 1 episode, 1 on DVD in UK, 0 elsewhere - 100% (UK), 0% (World)
Ninth Doctor - 13 episodes, 13 on DVD - 100%
Tenth Doctor - 44 episodes, 44 on DVD - 100% (includes mini-episodes, but not animated ones)
The Companions:
Susan - 51 episodes, 23 on DVD - 45%
Ian & Barbara - 77 episodes, 29 on DVD - 38%
Vicki - 39 episodes, 12 on DVD - 31%
Steven Taylor - 45 episodes, 4 on DVD - 9%
Katarina - 5 episodes, 1 on DVD - 20%
Dodo - 19 episodes, 3 on DVD - 16%
Ben & Polly - 40 episodes, 9 on DVD - 23%
Jamie - 113 episodes, 35 on DVD - 31% (including The Two Doctors, 33%)
Victoria - 41 episodes, 10 on DVD - 24%
Zoe - 50 episodes, 17 on DVD - 34%
Jo Grant - 77 episodes, 24 on DVD - 31%
Sarah Jane Smith - 80 episodes, 36 on DVD - 45% (including The Five Doctors and with the Tenth Doctor, 48%; with spin-offs, 54%)
Harry Sullivan - 28 episodes, 16 on DVD - 57%
Serials not yet released on DVD
First Doctor
The Keys of Marinus
The Sensorites
Planet of Giants
The Rescue
The Romans
The Space Museum
The Chase
The Ark
The Gunfighters
Second Doctor
The Dominators
The Mind Robber
The Krotons
The War Games
Third Doctor
The Ambassadors of Death
Terror of the Autons
The Mind of Evil
Colony in Space
The Daemons
Day of the Daleks
Curse of the Peladon
The Mutants
The Time Monster
Frontier in Space
Planet of the Daleks
Invasion of the Dinosaurs
Death to the Daleks
The Monster of Peladon
Planet of the Spiders
Fourth Doctor
Revenge of the Cybermen
Terror of the Zygons
The Android Invasion
The Seeds of Doom
The Masque of Mandragora
The Deadly Assassin
The Face of Evil
Image of the Fendahl
The Sun Makers
Underworld
The Creature from the Pit
Nightmare of Eden
The Horns of Nimon
Meglos
Full Circle
State of Decay
Warriors' Gate
Fifth Doctor
Kinda
Snakedance
Mawdryn Undead
Terminus
Enlightenment
The King's Demons
The Awakening
Frontios
Planet of Fire
Sixth Doctor
The Twin Dilemma
Attack of the Cybermen
Seventh Doctor
Time and the Rani
Paradise Towers
Delta and the Bannermen
Dragonfire
The Happiness Patrol
Silver Nemesis
The Greatest Show in the Galaxy
Serials Impossible to be released on DVD without animated reconstruction
First Doctor
Marco Polo (0/7 surviving)
Reign of Terror (4/6 surviving)
The Crusade (2/4 surviving)
Galaxy Four (0/4 surviving)
Mission to the Unknown (0/1 surviving)
The Myth Makers (0/4 surviving)
The Daleks' Master Plan (3/12 surviving)
The Massacre of Bartholomew's Eve (0/4 surviving)
The Celestial Toymaker (1/4 surviving)
The Savages (0/4 surviving)
The Smugglers (0/4 surviving)
The Tenth Planet (3/4 surviving)
Second Doctor
The Power of the Daleks (0/6 surviving)
The Highlanders (0/4 surviving)
The Underwater Menace (1/4 surviving)
The Moonbase (2/4 surviving)
The Macra Terror (0/4 surviving)
The Faceless Ones (2/6 surviving)
The Evil of the Daleks (1/7 surviving)
The Abominable Snowman (1/6 surviving)
The Ice Warriors (4/6 surviving)
The Enemy of the World (1/6 surviving)
The Web of Fear (1/6 surviving)
Fury From the Deep (0/6 surviving)
The Wheel in Space (2/6 surviving)
The Space Pirates (1/6 surviving)