I'm actually not terribly enamoured with the word fandom to be honest. Still, as a geek, I'm definitely the most enthusiastic about Doctor Who when it comes to the media properties I could be watching. In fact it's probably the only show (other than maybe Sherlock) that I follow carefully enough to not miss any episodes and to be relatively up to date when it's airing new episodes (seeing each new one the week it airs if not the actual day). There are other shows that I collect on DVD, but Doctor Who is currently the only one I'm collecting on Blu-ray (partially for the special features). I rather do want Sherlock on Blu-ray as well, but that's a wish rather than a more highly prioritized want or need.
There are some questions that people ask pretty much any Doctor Who fan, and while my answers to some of these have changed over time, and while most pertain only to the new series (eg. 2005 and more recent episodes), these are my current answers:
Favourite Doctor: Eleven. This isn't just because Eleven was the first Doctor I really watched a LOT of, but I also like his aesthetic and personality. His energy, confusion, and fashion choices are all of interest as are the types of imaginative stories he takes part in.
Favourite Companion(s): Clara with Martha Jones in a close second place. I kind of wonder at this. I think Martha suited more of what I wanted/needed for myself at the time that I watched the episodes with her in them for the very first time. She suited my ideas of self and what I wanted to be at that point in my life when I was still surrounded by perpetual student-dom. But I think as I've gotten older, Clara has become more suitable for my personal desires/motivations. I really do like some of what has been done with the character and I like how she seemed so confident and strong (especially in the earlier episodes featuring her) but also has depth as a character and is unreliable (like most characters) and has weaknesses. Aesthetically Clara looks gorgeous and I would aspire to be just as beautiful as her at some point though I know I'll never be able to echo her precise style (partially because I'll never be that petite and doubt that I'd want to wear such high heels so frequently). Someday I'd like to cosplay as both Clara and Martha, and really want to own a leather jacket as gorgeous as Martha Jones'.
Favourite episode: Blink. It's a great standalone episode and features fabulous acting and storytelling. It's also the first appearance of the Weeping Angels.
Most favourite villain (reoccurring): The Weeping Angels. They are just so neat to think about and quite frightening for so many reasons.
Least favourite villain (reoccurring): The Daleks. And that doesn't mean I hate them, but rather that I don't like them. They're an essential part of the Who-universe and they feature prominently in some pretty essential episodes, but yeah.
A few other comments on Doctor Who: I realize that most Doctor Who seasons are uneven. There are a lot of episodes that I don't particularly enjoy or I feel prevent me from suspending my disbelief. But there are also quite a few good episodes each season. If I were to go through all the new Doctor Who episodes and tell you some of my favourite and least favourite episodes each season they would go as follows:
Series 1: The Empty Child/The Doctor Dances (two parter that is awesome on so many levels) and Rose (mostly because it feels hokey but I really do like the use of the Autotons especially now that I've seen the Classic Who episode that featured that villain).
Series 2: The Girl in the Fireplace (so gorgeous and so emotionally charged) and The Impossible Planet/The Satan's Pit (quite honestly I have issues with the whole proximity of a black hole thing plus the devil ought to not be a thing, really)
Series 3: Blink and Daleks in Manhattan/The Evolution of the Daleks (I dunno… as scary as it is, it didn't quite seem believable in certain ways.
Series 4: Voyage of the Damned (this Christmas episode was just plain awesome. Guest star Kylie Minogue made this episode a must watch for me) and The Unicorn and the Wasp (which I found rather hard to watch if only because I didn't find this murder mystery style tale as convincing)
Specials: The End of time (it's hard not to rate that one really highly) and The Next Doctor (which I just didn't enjoy the characters of nearly as much as of the other specials)
Series 5: The Eleventh Hour (one of my all time favourite episodes) and The Beast Below (which didn't sit right with me somehow)
Series 6: The Girl Who Waited (such an emotionally charged episode) and Night Terrors (quite frankly this is too disturbing for my sensibilities)
Series 7: Asylum of the Daleks (one of the only Dalek episodes that I actually really appreciate) and The Doctor, the Widow and the Wardrobe (which is one of my least favourite Christmas episodes if not my least favourite one)
Specials: Day of the Doctor and Time of the Doctor (hard to rank these but The Day of the Doctor is obviously the better of the two)
Series 8: Robot of Sherwood (which I loved because of how it dealt with Robin Hood) and Kill the Moon (which brought me entirely out of the story… ugh)
Series 9: Gosh… I can't be retrospective on episodes as they're still airing, can I?
Overall, Doctor Who is a wonderful universe and yes, I own a lot of Doctor Who merchandise (etc.) and have really been enjoying the graphic novels too.