They're all good.
The Tenth Planet
is a great story, has the Cloth Faced Cybermen, and the first Regeneration. We actually see just how alien the Doctor is when they introduce this Regeneration idea, and it truly was an innovative way to continue the show with a different actor/style of Doctor
The War Games
is a Great story, though quite long, and introduces us to the Time Lords. Tearful goodbyes to Jamie and Zoe who have their memories erased, forced Regeneration of the Doctor by his own people, simply for acting the Hero for the Galaxy. We don't actually see a Regeneration, but, it's great nonetheless.
Planet of the Spiders
- I'm surprisesd this story isn't more popular, I really enjoy it, but, I know many don't. It introduces us to the idea that Doctor might have trouble Regenerating, that it's not necessarily as simple as changing an outfit, he was in real danger of dying forever, until he was helped.
- The middle story in a Trilogy with the Return of The Master. Fantastic on it's own. We got another new element in The Watcher (IMHO, this gives credibility to seeing Doctors return older than they were when we saw them Regenerate. If the next Regeneration can exist before The Regeneration, then the previous one can also exist, somewhere, in an alternate reality continuing to age). Leads straight into Castrovalva.
Caves of Androzani
- One of the best Classic Who stories. The Doctor wasn't sure if he would be able to heal from Regenerating (With good reason, seeing as how he didn't Regenerate in Let's Kill Hitler
after being poisoned). He gave up his life voluntarily to cure his Companion, not like in other stories, where his life was taken from him by circumstances.
Really tough to single out any one of these as "THE BEST STORY", as they are all Classics that brought something new to the mythos, in addition to being a great send off for the previous Doctor. Sure, Planet of The Spiders
has the least impressive Regeneration effects, but, the Poll is asking for Best Story, not best effects. Can I have 5 or 6 votes?