There are several problems with staring at the "beginning" with the reboot in 2005. Problem #1: I'm not sure Eccleston was the best Doctor. This is terrible to admit, because he was my first Doctor, and I was one of the people he totally won over. His Doctor and Rose sucked me into the series so much that when he regenerated, I scoffed at the second season and insisted I was going to stop right there and not watch anymore, because I didn't need to see Barty Crouch Jr. and his googly eyes as the Doctor. My friend Joy--bless her Whovian heart--verbally smacked me across the face and told me in no uncertain terms that if I didn't give Tennant a chance it would be the worst mistake of my life. I think that might have even been the exact way she put it. So I watched Tennant, and suddenly I couldn't imagine there ever being a better Doctor...and then Matt Smith happened. So in my case I just love them all. But my point is that Eccleston is not for everyone, and I've heard so many times that the first season is boring, so... I'm not going to suggest you start with it.
Problem #2 is not so much of a "problem" as it is a helpful fact about the series. If you're trying to watch it linearly, you're not thinking like a true Whovian. Time, "from a non-linear, non-subjective view point...it's more like a big ball of wibbly-wobbly, timey-wimey stuff." So really, this is the perfect show to watch all out of order. It practically instructs you to do so.
Problem #3: if you're starting now, you've got a lot of catching up to do. There's a LOT of episodes these days. Some are better than others, some are necessities, and some you don't really need to watch at all unless you're a die hard fan and love every line ever written in connection with the series. Which not everyone is.
Now, really quickly, before we get into my proposed, hacked-up order of episodes, I want to link to the namesake of my Machete Viewing Order of Doctor Who: the Machete Viewing Order of Star Wars. I like it.
Now, back to the Doctor.
I suggest everyone start with season 3, episode 10: "Blink." It introduces the basics of time travel, but gently, and you learn it piece by piece along with a one-episode-only character, Sally Sparrow (played by Carey Mulligan, so there's another reason to watch it right there). You get exposition, but in a way that makes it more fun than any other exposition you've ever experienced in your life. You get introduced to--in my opinion--the best Monster the series has, and if you stick with the series, you get to see them again later on, with Matt Smith's Doctor. And it's just a phenomenally well executed episode.
Once you're done with Blink, head back to the beginning of season 2, and go from there. If you want just the highlights and want to buzz through it faster, my suggestions are below, but understand that true fans will inevitably howl at one or more of my choices to "not suggest" watching particular episodes. This is just my opinion.
- 3x10 Blink -- No arguments, just shut up and watch it.
- 2x00 The Christmas Invasion -- Necessary to introduce characters and watch the regeneration.
- 2x01 New Earth -- Classic early Tennant, and important getting-to-know-you between Doctor Ten and Rose.
- 2x02 Tooth and Claw -- Not mandatory, but a good historical setting, and more initial chemistry between Ten and Rose.
- 2x03 School Reunion -- A little bit more mandatory, especially if you're a Buffy fan. You get a sense of Doctor Who's history, meeting a companion from the 1970s.
- 2x04 Girl in the Fireplace -- Spaceships, history, and a really beautiful look at the loneliness the Doctor sometimes finds himself enduring, and bestowing on others. Great episode, great Monster.
- 2x08 and 2x09, The Impossible Planet and The Satan Pit -- Two-parter that is beautiful visually, and takes a good look at what the Doctor believes. Great performances.
- 2x12 and 2x13, Army of Ghosts and Doomsday -- Two-parter season finale.Classic Who Monster: the Cybermen, and wraps up Rose's storyline. Try not to cry in the final five minutes. I dare you.
- 3x00 The Runaway Bride -- Necessary to introduce a future companion, back when she was just a one-shot guest star. But Catherine Tate was so phenomenal that she ends up returning for a later season. Stay tuned.
- 3x03 Gridlock -- If you really feel the need to be introduced to Martha, the new companion, in her first episode, run back to 3x01, but otherwise, you can jump straight here. Interesting culture, and you need to meet the Face of Boe.
- 3x08 and 3x09, Human Nature and The Family of Blood -- Two-parter that showcases Tennant's acting talent, and gives you a glimpse of what the Doctor would be like if he were just a man and not a kickass Timelord. Again, I dare you to not have feels. It's impossible.
- 3x11 through 3x13 are kind of optional. I didn't respond to them AS MUCH but if you love Martha, watch them. The season finale two-parter 3x12 and 3x13 are heavy with series mythology, too.
- 4x01 Partners in Crime -- The return of Catherine Tate as Donna Noble. She's my favorite companion, so I'm partial to this episode. Plus? Cute Monster for a change.
- 4x03 Planet of the Ood -- One of the best Monsters ever on this show. Very cool.
- 4x07 The Unicorn and the Wasp -- An Agatha Christie murder mystery, the 1920s, and Donna Noble hilarity.
- 4x08 and 4x09, Silence in the Library and Forest of the Dead -- Not optional! Must watch. You are introduced to an extremely important character, and this is another amazing Monster.
- 4x10 Midnight -- Chilling, well-written, and great performances. (Colin Morgan guest stars!)
- 4x12 and 4x13, The Stolen Earth and Journey's End -- season finale two-parter with a zillion guest stars. Again, heavy on the mythology. Classic Monster: the Daleks. Sort of a farewell to Tennant, who you will be completely devoted to by this point.
- Waters of Mars -- Between seasons 4 and 5. Pretty decent Monster, but kind of optional.
- End of Time Parts 1 and 2 -- The final farewell to Tennant. Loads of returning characters from episodes past, mythology, and Timothy Dalton.
- 5x01 The Eleventh Hour -- Regeneration and introduction to Matt Smith's Doctor and his companion, Amy Pond.
- 5x02 The Beast Below -- You get to see what Amy Pond is made of.
- 5x04 and 5x05, The Time of Angels and Flesh and Stone -- Mandatory! The Weeping Angels from Blink are back! Awesome two-parter, heavy with mythology but SO well-executed. One of my favorite episodes. Plus? More River Song from 4x08 and 4x09.
- 5x10 Vincent and the Doctor -- Van Gogh and the Doctor. Fun, but I suppose if you're in a rush you could skip it if you absolutely had to?
- 5x12 and 5x13, The Pandorica Opens and The Big Bang -- Mandatory! Season finale two-parter with mythology, history, sacrifice, hilarity, plot twists, and--oh, just watch it already. :)
- 6x01 and 6x02, The Impossible Astronaut and Day of the Moon -- Mandatory! Lots of mythology in a season dependent on mythology. This is the stuff you have to watch in the order in which they give it to you. And oh, the feels!
- 6x04 The Doctor's Wife -- A love letter to the TARDIS, the Doctor's best and constant companion. Lots of hilarity and feels.
- 6x05 and 6x06, The Rebel Flesh and The Almost People -- Must watch for the mythology, and for the great performances by guest stars and Smith.
- 6x07 A Good Man Goes To War -- Mythology! So much of this season is woven through the episodes that it's difficult to skip any.
- 6x08 Let's Kill Hitler -- Mythology! And history, and hilarity.
- 6x11 The God Complex -- Introspective look at the Doctor, and a cool setting for the episode.
- 6x12 Closing Time -- One of the best stand-alone episodes, and a celebration of the silliness of Eleven.
- 6x13 The Wedding of River Song -- Mandatory! Heavy mythology, wrapping up a truly ingeniously woven-together season.
- 7x01 Asylum of the Daleks -- Necessary introduction to a returning character, classic Dalek episode without it being overly-Daleky.
- 7x05 The Angels Take Manhattan -- Farewell to Rory and Amy! And Weeping Angels, so....awesome. :)
- 7x06 The Snowmen -- Reintroduction to the new companion.
- 7x10 Hide -- Creepy haunted house, good Clara episode.
- 7x11 Journey to the Centre of the TARDIS -- Clara mythology, and another love letter to the TARDIS in episode form.
- 7x13 Nightmare in Silver -- Showcases Smith's acting ability, and some good Eleven/Clara moments.
- 7x14 The Name of the Doctor -- Wraps up Clara's storyline, and is important, mythologically speaking.
So there you have it. You're caught up. I shaved it down from 102 episodes to a more manageable 52. Almost half! When you're done, if you're inclined, go back and fill in the gaps. Every episode is worthwhile, in my opinion. :)
And if you want to get in awesome shape by the time you're done with all of these, here's my Doctor Who exercise game! </shameless self promotion>