Alright, this is going to be tough. I grew up with PBS rerurns of Pertwee, Baker and Davison, and in a way, they are all "my" Doctor, just as Eccleston and Smith are in the current era. There isn't a single Doctor that I actively dislike, though there are specific ones that are near and dear to my heart for various reasons. Ranking them individually is going to be exceeding difficult.
1) Christopher Eccleston
2) Jon Pertwee
3) Matt Smith
4) Peter Davison
5) Tom Baker
6) Patrick Troughton
7) Paul McGann
8) David Tennant
9) Sylvester McCoy
10) Colin Baker
11) William Hartnell
That list is inaccurate in many ways, but it's about as close as I can get to codifying how I feel at this moment. And it's only representative of how much I enjoy the actor's performance and their Doctor's character, not at all about the stories they were in. For many years, I probably would have put Tom at the top of the list, simply because I saw the most of him growing up. But as I've gotten older, the nostalgia of the first time I saw Pertwee has superseded that; likewise, Smith could have ranked at the top, but the...disjointed, frenetic atmosphere of series 7, as well as all the angsty anticipation of his departure, has actually dulled my appreciation. Hopefully that will change sometime in the future.
But what will never change is how, in 2005, Christopher Eccleston grabbed me from his first line. In that instant, he became the Doctor to me, and it was like meeting an old friend again, for the first time. It took me until "The Girl in the Fireplace" to really warm to Tennant, and until the end of "The Eleventh Hour" for Smith to solidify as the Doctor for me. But Eccleston had me at 'hello.' Literally. That's never going to happen again, no matter how good any future Doctors may be. It just can't.
As far as eras, in terms of overall fun of stories, it's the Hinchcliffe era, Pertwee's first year, Moffat's writing during the RTD era, and the first two years of Amy & Rory.
Speaking of which... Companions. That's much easier for me. Rory is number one in my book; by the time "Let's Kill Hitler" rolled around, Rory had thoroughly supplanted Amy and Martha as my favorite new series companions, and he really is my favorite companion of all time. So...
1) Rory
2) Sarah Jane
3) River
4) Jamie and Amy (yes, the Scots tie)
5) Martha
6) Leela and Liz (another tie)
7) The Brig
8) Ace
9) Turlough
Note that I haven't seen any of Jo Grant (barring her appearance on SJA) since I was a kid, so until I see anything from Terror of the Autons through The Green Death again, the jury's going to be out there. I've also never (to my recollection) seen any of Ben & Polly, or Mel, and nowhere near enough Ian & Barbara to render a judgement.
And yes, I know some people don't count River or the Brigadier as companions, but I do. So there. :P
