This is actually incredibly difficult for me to answer! The first reason for that is that I haven’t watched every episode of DW, including the high, high majority of Classic Who. I’ve been meaning to get to all of Classic Who, but I’ve only really touched a few episodes with the First Doctor at this time. It’s also been a moderately long time since I’ve watched Nine and Ten, so it makes it harder to compare.
Consequently, I really could put Nine, Ten, and Eleven in different orders on any given day. Odin, if I were answering this question in a different hour, I’d probably put them in different orders! I do like all those Doctors very, very much.
1. Eleventh Doctor. I know the fandom sometimes seems to be on an opinion split regarding Matt Smith. Some people love him, some people don’t. Matt Smith is my first Doctor (though I watched most of Nine before I went through Series 5 and onward) and he’s consequently the one who pulled me into the fandom. Matt Smith’s later seasons have some glitchy writing in my personal opinion, but when this Doctor is written well, he’s written well. And Matt can make any script fall into the character of his Doctor. It’s cool. And I think that Series 5, the first season with Matt as a Doctor, is my favorite all-time of Who. There is some downright stellar stuff with that. I can’t help but love a quirky, cheerful, nutty Doctor like him; he’s what I think of when I think of the show. The Raggedy Doctor is my Doctor.
2. Tenth Doctor. I actually haven’t seen every episode of Tennant, but I have seen most, and he has some real stand-out moments. Like when he is the human John Smith. That episode is just one big “wow.” One BIG wow. The writing for the Tenth Doctor is some of the best in Doctor Who, so his character is well-done. He’s a bit of an amusing nut, but he’s oh-so-noble, and feels so personable and “human”(oid). I think that makes him great.
3. Ninth Doctor. Sometimes I feel like this guy is so underappreciated. Nine is a Doctor full of depth, personality, humor, and buttkicking. I really love this guy and get extraordinarily excited when I meet other Nine adorers. Honestly, I just see the twinkle in his eye and squeal, “NINE!”
4. Twelfth Doctor. I’m not going to try to list off the Doctors from Classic Who, even though I’ve seen more than a few of them at comic conventions, and they’re great personalities. But as far as on-screen Who is concerned, I’m only going to talk New Who. And I think Capaldi is great. I’ll admit I don’t like the episodes that much for him (okay the Robin Hood episode was entertaining!), but I do enjoy Capaldi’s acting. I like this whole gruff, obnoxious, socially unfit version of the Doctor. And as someone who studies philosophy in college, I find his internal ethical theory downright fascinating. It’s honestly a really cool philosophy and perspective on ethics we don’t see portrayed enough on screen.
5. The War Doctor. John Hurt’s Doctor does not intrigue me as much as the others, but he should be appreciated for sure. I mean really. He does a good job, and he really adds to the dynamic of all the Doctors in the 50th Anniversary special. His pragmatism and seriousness is a great contrast from Matt and Tennant bumbling around on screen. He shows what it means to be a man within conflict very well.