The break until the 50th gives me a great opportunity to catch up on Classic Docs. While there's some great and imortant episodes, there's also a lot of... drawn out tediousness in the early days. I'm making a list of 'must see' episodes for those interested in checking out important or fun developments in the history of the Doctor, and will include updates on my list from time to time.
Here's my thoughts so far on shows I'd definitely recommend:
An Unearthly Child - The Very first story! While it might be fun to watch the entire serial, Part 1 is the most important to see the introduction of the Doctor, his granddaughter Susan, and Ian and Barbara.
The Daleks - The second story is the first for the Daleks! The entire serial is wonderful. Watch it all!
Dalek Invasion of Earth - Also very good, an important continuity point, and features a poignant moment for the Doctor and Susan, his famous "Some day, I will come back" speech.
The Romans - Okay, not much important happens here continuity wise, but the episode is (intentionally) hilarious!
The Ark - Good storytelling, good mystery, and good use of Time!
The Tenth Planet - About to be released with animation filling in the 'lost episodes'. Not only does this introduce the Cybermen, but features the Doctor's First Regeneration. The cybermen are very different than the modern ones, but SUPER creepy!
Tomb of the Cybermen - Good sample of Second Doctor and dynamic with companion Jamie. Plus Cybermen!
Web of Fear - If you can find parts to watch, it features the Great Intelligence, and the introduction of Lethbridge-Stewart.
The Invasion - More Cybermen! The beginnings of UNIT! The Brigadier! Somewhat slow moving story, but some important elements. And a VERY creepy human villain!
The Seeds of Death - Ice Warriors!
The War Games - A very long 10 part serial. If you're looking for a drive-by, just cut to the final episode or two, which features the introduction of the Time Lords as a people, explains why the Doctor sole the Tardis and ran away, and finds himself penalized, forced to regenerate, and exiled to earth.
Spearhead from Space - Color! This episode is awesome. For fun, watch this back to back with the revival series' S1E1, "ROSE". There are a ton of parallels.
The Silurians - Intro to the Silurians! Back before we learned that every face we saw of theirs was really a mask hiding humanoid features, a la Vastra.
I've just begun Season 8, which introduces The Master... more reports and suggestions later.