And a good laugh when they get sealed back in. 
Well, y’see, they have certain qualities that appeal to me beyond their acting. As Jamie is a guy it doesn’t work like that.
Unfortunately the 1st and 2nd Doctors are the ones I’ve least watched so far. From Hartnell’s time the serial I liked best was The Daleks’ Master Plan which is the most epic Who I’ve ever seen. However it is very long (13 episodes).
Pertwee just maybe my favorite Doctor. I’ll second Terror of the Autons, which was the first Master story and also introduced the delightful Jo Grant and add The Curse of Peladon, Day of the Daleks, The Sea Devils (another Master story, and one of the best. He swordfights the Doctor and one of his scenes was referenced in The Sound of Drums) and Carnival of Monsters (great dialogue despite the horrible visuals). I agree with the posters who suggested The Daemons and The Time Warrior but I think it’s probably best to watch The Green Death before Planet of the Spiders.
The stories I’d recommend skipping on the strongest possible terms are Colony in Space (derivative and boring), The Mutants (unbelievably stupid), The Time Monster (despite three great scenes by the Doctor this is one of Who’s all-time worst), Frontier in Space (it’s a tragedy this was Roger Delgado’s last appearance as the Master, to me none of the others ever came close) and the other 2 Dalek stories ( which always make me think they wanted to have Daleks but couldn’t be bothered to think of a story for them).
All of the above is obviously very much IMHO. Others’ mileages do vary.
He wears a skirt. What more can you want?
If you haven’t already, check out “The Three Doctors,” in which the Time Lords bring back Hartnell’s and Troughton’s Doctors to assist Pertwee’s version in battling an existential threat. Unfortunately, Hartnell was in very frail health and it shows, but there is some great interplay between Troughton and Pertwee. Yeah, the plot, effects, and sets are all a bit wobbly, but if you’ve been watching Who for a while, you can handle that.
For Hartnell’s era, try watching the opening episode (“An Unearthly Child”). If you can pretend that it’s 1963 and you know nothing about Doctor Who, it’s quite a treat. It’s a world apart from the “Rose” (the 2005 opener), going for an eerie atmosphere and slow reveal rather than athletic, whiz-bang adventure (and of course not a spot of CGI). Yeah, it’s slow. The whole episode is just introducing the characters and establishing the premise, but it’s very well done. I found it interesting to see how some characteristics of the show have changed and others were established right off the bat and held fast. Skip the rest of the serial (a dull, somber affair featuring cavemen) and head straight for the second adventure, “The Daleks.” (That’s exactly what the first Doctor Who novelisation did, by the way.) Pretend that you’ve never seen a Dalek before, as the slow reveal is part of the fun. The title creatures are much weaker and more limited in ambition than in later stories, but somehow scarier. Ian (one of the Doctor’s companions) is the hero of this adventure. The Doctor is still not entirely to be trusted.
What intrigued me most about the Hartnell era episodes is that the Doctor, despite being the titular character, is not really the hero or even the main character. Ian & Barbara are clearly the heroes whom the audience is meant to sympathize with. Ian in particular is the dashing leading man who solves problems, stands up against injustices, fights the good fight - all the things that modern day viewers would expect of the Doctor. Meanwhile, the Doctor himself is selfish, devious, egotistical, only too willing to abandon his traveling companions in order to save himself - a lot like Dr. Smith from “Lost in Space”, only less campy. Credit Hartnell, who was a well known character actor, with making the rather irresponsible Doctor as endearing as he was.
Ian’s anti-pacifism speech in “the Daleks” is also interesting in a “how times have changed” sort of way. It’s odd to see the gallant hero argue in favor of aggressively attacking an enemy rather against it. It should be noted that when the original Dalek serials (“the Mutants” & “Dalek Invasion of Earth”) aired, it was not that long after WWII. (18 years, about the same length of time between, say, the first gulf war and today.) While we see the Daleks as simply ‘goofy kitsch robots’ now, the idea of humans devolving into uniformly fascist creatures and invading London might have struck a nerve with audience members who remembered the nazi blitzkrieg.
What is mostly forgotten about the show is that it originally was conceived as a historical show - the Doctor & co. would visit different periods in Earth history rather than traveling to different worlds or the future. “The Aztecs” is an interesting historical adventure - not only does it have a strong story & well thought out characters, but it also takes time for character development, and to reflect on some interesting themes (the sharp contrast in Aztec & ‘modern day’ morality, Barbara’s attempts to change history by banning human sacrifice.)
As for Patrick Troughton’s era, the “Discontinuity Guide” once remarked, this was an era when the producers became more cost-conscious. Writer Terry Nation, who created the Daleks, banned their use on the show (he hoped to base his own show around them), and the producers were scrambling to create a new gimmicky monster they could merchandise the same way.
Also, as a cost cutting move, stories became routinely longer (6-8 episodes the norm) in order to cut down on the expense of creating new sets. The problem being that most of these longer serial were overly long, obviously padded and tend to lose steam halfway through. Stories also became more formulaic as well - a gimmicky monster attacks an isolated outpost with a small group of humans, the Doctor & companions arrive, monster picks off humans, Victoria screams a lot, Doctor saves the day & departs. Repeat in next story.
Actually, it’s a credit to Troughton’s portrayal that the series survived this period. Props also to the actress who played Zoe, she was a spunky companion. (Victoria seemed a little useless though.)
Although this one is at least partly redeemed by the ample charms of Ingrid Pitt on display in the last two(?) episodes.