First impressions are important.Leaving aside (W)ho's your favorite Doctor,which story did the best job of introducing a new Doctor and was a great story in its own right?
I'd give the gold medal to An Unearthly Child.It had double duty in introducing not just a Doctor,but the show itself,and did so brilliantly.Maybe the best single episode of the entire run of the show.
The silver goes to The 11th. Hour.The Tennant/Davies era was a tough act to follow,but Smith and Moffat pulled it off with ease.
The bronze:Robot.It's a Third Doctor kind of story,but with Tom Baker in the lead,it feels nothing like a Third Doctor story.Shows how crucial casting a Doctor is.
As for the others,Power Of The Daleks sounds like a lot of fun.
From a DVD review of Spearhead From Space:A awe-inspiringly assured debut from Jon Pertwee,and some inspired visuals,have raised an average story to greatness."
My thoughts exactly.
Castrovalva;such a clever idea,but where's the fun? A question that gets asked a lot during the '80s.
The Twin Dilemma and Time & The Rani both show JNT's passive-aggressive attitude about the show. Debuts should show off new Doctors in the best possible light,but these are two of the worst stories this show ever had. Somebody didn't want to be where they were at.
The TV Movie had its problems,but McGann wasn't one of them.Nothing against Eccleston,but it's a shame McGann couldn't have been brought along for the new series.
But we got Eccleston,and we were lucky to get him for Rose.Couldn't keep him though.
If you're introducing a new Doctor,it's probably a mistake to keep him sidelined for much of The Christmas Invasion.Tennant did make the most of what time he did get.
As for Deep Breath,Capaldi gets a thumbs up,but Moffat likes to reuse story ideas,doesn't he? At least they're good ones,and he knows how to get the most out of them.

The two best first episodes are "Rose" and "An Unearthly Child," hands down.

"Robot" is amazing as far as Tom's debut goes, but the plot otherwise is weak.

"The Eleventh Hour" is a strong followup.

I can only speak of the three latest Doctors.

Rose was the first ever Dr Who episode I ever watched, and I did mostly because I felt that there were some credits missing in my Geek Belt by never having watched Dr. Who. It took me a long while to warm to the show and the character, so I can't say Rose would be my answer.

I did end up liking Eccleson a lot, so by the time I got to The Christmas Invasion, I wasn't convinced I would like Tennant. It also took a while for me to warm up to him.

When I first saw a picture of Matt Smith when he was announced, he looked like some sort of punk/goth moron. I immediately hated so I was already biased against him. By the time The Eleventh Hour finished I said "Holy Crap, Smith is awesome" It remains one of my favorite Who episodes ever.

So, TEH by a mile, for me.

I like Eccleston a lot, but I don't think "Rose" holds up all that well. I like The Eleventh Hour more.

The Christmas episode that introduced David Tennant was pretty weaksauce, since he was hardly in it, but it got better after that one.

the correct answer for any Dr Who question is Tom

"My Generation."

Oh, Dr. Who...never mind.

Most of them suffer from either: a) the Doctor spending too much time recovering, so it's carried by the companions (Castrovalva, TV Movie, Christmas Invasion) or b) it's a weak story (Robot, Twin Dilemma, Time & The Rani).

An Unearthly Child and Rose don't deal with the regeneration aspect, so in my mind, they're lacking that essential quality. They're great, but have asterisks next to them.

In my view, the ones that have the best balance of regeneration and good story are Spearhead From Space and The Eleventh Hour. Both get points for featuring the Doctor stealing his new outfit from a hospital.

I liked Christmas Invasion more for the farewell than the introduction. Altho, tea being the secret ingredient to revival is AWESOME!

The Eleventh Hour has both a fabulous farewell and intro. Some batshit crazy, bad hair - not a ginger, lots of running and stuff, a long story mystery and Rory.

I think they have figured out how to do it right.

I do have to give props to An Unearthly Child. That is still one of my favorite stand alone episodes.

The very first episode of the first adventure, "An Unearthly Child". Christmas Invasion and Eleventh hour come close though. C.I. was brilliantly done--so much so, that when you finally got to Tennant in all his glory on the Sycorax ship, it was almost the best ever exploration of a newly regenerated Doctor. First episode of Robot was pretty excellent as well for its showcasing of Tom Baker.

"I'm the Doctor. Run for your life!"

I've only been watching since the nu-Who started, but that pretty much hooked me.

When Troughton first appeared, that had to be mind blowing for Who fandom. Thank goodness it worked. A shame that the video of the episode and the adventure are lost to us.

When Pertwee showed up they changed the tone of the show drastically and went to color all in one fell swoop and the regeneration was almost lost in the mix.

I think Tom Baker got the most benefit of any Doctor's first episode. The whole process was old hat by now and following Pertwees' 5 year run, it was a really big event and Tom didn't let us down.

Davison got the short end of the stick, being A) too young for the role (him personally for the time), B) having to follow Baker's seven year run and C) being saddled by being bland, weak and JNT.

Colin Baker was also saddled with a bad story and JNT, ditto McCoy.

Eccleston had a good opener with good bits but his silly side of the Doctor never worked that well, nor did the comedy with him. Not at all. Each opener since has gotten better and better.

Colin Baker said, "I am The Doctor, whether you like it or not".
That seemed soooo perfect to me. My favorite ever.
Too bad about BBC, or whatever at the time, did all in it's power
to destroy him and the franchise.

JNT?

John Nathan Turner (IIRC) a Producer and Writer and (once again IIRC) constant foil to BBC.

NOT a writer. A bean counter who foisted Really Bad Ideas onto the writers.

A bean counter and a guy with really horrible taste in clothes. And costumes. And not real good at producing.

Thanks for the corrections.
I was doing it from memory during Colin's original run.
My other (possibly more accurate) description was
based on the fan press at that time:
a spawn of a union between Hitler and Satan,
hired by the BBC to destroy the Dr. Who franchise
and if possible all happiness in the UK.

Michael Grade, then head of the BBC had publicly made it known that he wasn't a fan of the show in the first place---not a good thing to say publicly---and that it was "old and tired", said the man with an agenda. I think the whole thing became a self fulfilling prophesy at that point. It had become majorly uncool, the budget kept getting cut, the number of episodes got cut down, etc. Plus, it was being compared to newly emerging shows like ST TNG, who were spending 50 times the money on the show. There should have been a major rethink and reorganization but they just let it flounder and gave it no love. JNT, for all the abuse I'm ready to give him, did love the show. He wanted to move on after Colin, move on to furthering his career and the Beeb told him that if he leaves, they'll just cancel the show. so in his favor, he stayed on to make sure the show still existed and they got three more years out of it. Which was good because if the show disappeared after the Trial of a Time Lord season, that would have been a shame. Colin's first season, I thought was very good, the second, not so much.