I've never followed this franchise. What are the average number of episodes per season? how many doctors have there been? What has been the presence of minority actors?
What is the "best" era to start off with for beginners?
I'm no expert really. I've watched some episodes, but I haven't been consistent at all. The BBC series have short seasons, so it's about 12 episodes per season (or the British call a season a series so that can be confusing). There are 13 Doctors (with 13 being the new Doctor, Jodie Whittaker). I don't know about the overall presence of minority actors, but I think it's a safe assumption that the show from the 60s-80s didn't have a lot of important or recurring non-white actors. With the revival of the series in 2005, I know that there have been at least three black 'companions' (Mickey, Martha, and Bill) of The Doctor, who assist him in his adventures across space and time.
The series was revived under the Ninth Doctor (there are 13 Doctors now) with Chris Eccleston (Malekith from Thor: The Dark World) as the Doctor. That might be a good place to start. He did like a season, and then David Tennant (Purple Man from Jessica Jones) took over. Tennant was very popular with fans from what I gather. Also Matt Smith, the Eleventh Doctor seemed to be popular as well, and I gather Peter Capaldi (12th Doctor grew on people).
I liked the Ninth Doctor, though I only have seen one episode with him. He was a darker take on the character. Tennant annoyed me, but the fine Martha was his companion so that's a point. Smith annoyed me at first, but I came to like him. And I had to rethink my dislike of Tennant when him and Smith teamed up for the 50th anniversary episode, "The Day of the Doctor" which I thought was really good and a nice nod to the history of the character, and I'm not even a Doctor Who head like that. I watched a little of Capaldi but couldn't get into his run so I haven't watched the show in a while.
What I do like about the concept overall is the Doctor regenerates into a new incarnation so it's a cool way to do recasting when needed and keeps all the shows connected to some extent. I also like the time travel aspect of the show, which could have some educational value. I also like many of the villains, like the Cybermen. I mean, sometimes the villains are goofy or look cheaply conceived or made, but they have a charm about them, and it's interesting to see a non-American perspective on sci-fi.
I got more into the Who spin off Torchwood than the actual Dr. Who. This was a darker, more adult take on the material, which followed the alien hunting team from the Torchwood organization. I watched the first two seasons. The third season (series) was only like five episodes, "The Children of Earth" and I thought it was the high point. The fourth season, "Miracle Day" is one I haven't finished. The Torchwood team comes to America and Mekhi Phifer is also involved. There wasn't a steady black character on Torchwood's earlier seasons, though Martha Jones was like a recurring character for a bit. Whereas Dr. Who is more of a family friendly show, Torchwood is more adult oriented to let you know.
There have also been at least two other Who spin offs: The Sarah Jane Adventures and Class. I haven't watched either.
http://tardis.wikia.com/wiki/Ninth_Doctorhttp://tardis.wikia.com/wiki/Tenth_Doctorhttp://tardis.wikia.com/wiki/Eleventh_Doctorhttp://tardis.wikia.com/wiki/Twelfth_Doctorhttp://tardis.wikia.com/wiki/Thirteenth_Doctorhttp://tardis.wikia.com/wiki/The_Doctorhttp://tardis.wikia.com/wiki/Martha_Joneshttp://tardis.wikia.com/wiki/Mickey_Smithhttp://tardis.wikia.com/wiki/Bill_Pottshttp://tardis.wikia.com/wiki/Torchwood_(TV_series)http://tardis.wikia.com/wiki/The_Sarah_Jane_Adventureshttp://tardis.wikia.com/wiki/Class_(TV_series)