Wew people speculating about the Fourteenth Doctor already. Imagine if the show got cancelled after Whittaker and we had to wait for a crappy TV movie
However nonetheless, some choices off the top of my head:
David Harewood
I've mentioned Harewood in my picks for the 13th Doctor. He has such an alien look and has experience playing an alien character, being Martian Manhunter in Supergirl. I could see him playing a more down to Earth, but a quite ancient, dignified Doctor. Whilst there's plenty of room for humour, it would be more subtle and calm than we've been used to in NuWho, so a new bunch of writers that don't revert to Tennant-Smith zaney writing would be needed to do this Doctor justice.
Charles Dance
After the young and presumably energetic, bubbly Jodie Whittaker, it would be nice to return to an older Doctor. I could see Dance embody both the Doctor and the Master very well, but for the sake of this page lets talk about him as the Doctor. I could see him being an older, more serious Doctor, and would be stern in a similar manner to William Hartnell and Jon Pertwee. Again, writers that didn't default back to zaney Tennant-Smith styles would most definitely be needed to do this Doctor justice.
Damien Molony
Someone I haven't shut up about as the Doctor since before Matt Smith even announced was leaving, Molony was my top pick for the next Doctor for a long time. There's a variety of different directions Molony could go as a Doctor, he could easily play a posh romantic, another anchient-young Doctor but less of the quirky weirdness of Smih and instead a timed out tired Doctor, he could also be quite alien in a posh aristocratic way imagine. I imagine the humour with this Doctor to be a bit similar to Thor's in the Marvel Cinematic Universe for some reason (not however I have not seen Ragnarok yet). They could get away with writing Molony in a zanier way than the two options above I guess.
Nigel Havers
Someone else I've talked about as the Doctor for quite a long time, although not as long as Molony. I'm not as hot on this choice as I once was, but I'd still be happy to see him in the role. To my mind, he'd be a Doctor very reminiscent of Jon Pertwee...maybe it's the voice. I could see him play a charming, maybe another dandy Doctor too. However maybe Havers doesn't have the calibre to pull off the role, I'm not sure, his roles in the past as far as I'm aware haven't quite been at the same level as something such as Doctor Who.
Jason Flemyng
Ginger at last! Someone else I've talked about being the Doctor since prior to Matt Smith leaving, has sort of alternated between him, Molony and Idris Elba (who I no longer see as quite the right choice for the Doctor) being my top choices for the role for a long time. I could see Flemyng pull off a vast variety of different Doctors, I could most easily see him playing a rather jokey, cheeky Doctor however. I imagine the usual NuWho zaney writing would work with Flemyng, if they didn't want to stray too far from the traditional style of writing, Flemyng could be a pretty good choice.
Ben Daniels
Runner up for the Twelfth Doctor, I reckon Daniels deserves a shot at the Doctor again. After seeing snippets of him in the (what I found to be boring) Exorcist series, I think he has the gravitas for a role such as the Doctor. I could see him hark back to "tougher" Doctors like Eccleston, definitely worth being taken a look at for the Doctor again.
That's all I can think of for now. As you can tell, I don't particularly want another young energetic "tigger" Doctor, and have chosen (other than Molony) varying degrees of older Doctors, most of them of which would be calmer and more restrained by NuWho standards. As you can also see, there are no women on this list. I was against the casting of a woman as the Doctor, mostly out of fear over how the writing would handle it (here's hoping Chibnall can deal with it maturely) along with the casting being made purely out of feminist agenda and a desperate grab to get ratings up again. However I've sort've gradually become less...wary of the gender switch, and I'm not one of the "I'll never watch the show again" fans. However for the purposes of this list I simply cannot think of a woman I'd cast as the Doctor, and also after the first female Doctor I think it would make sense to go back to a male Doctor (if any of you brand me sexist for this, reminder Chibnall was
only ever going to cast a female Doctor). Honourable mentions though would be Eva Green (who would have been my joint top choice for a female Doctor, but I'd by
FAR prefer to see her as a Master/Missy, as I feel she'd portray a bad guy far better than a goodie, she'd be wasted as a Doctor when she could be a Master. Unlike Missy, she could actually play intimidating and sinister very well, and actually make the character feel like a threat again), and my second female honourable mention would be Hayley Attwell, who initially I'd have preferred to see as a companion, but nowadays I'd be open to seeing her as a Doctor, but I stand by my reasoning that it would make sense to have one or two male Doctors in between two female Doctors (in the future, maybe as the 15th Doctor I'd be very enthusiastic to see her in the role). Another honourable mention would be Idris Elba, who I once wanted as the Doctor but after further thought have decided it wouldn't really quite work that well. Same goes for Danny Dyer which I remember suggesting for 13, which in hindsight is a pretty crappy idea. I can't think of a specific actor, but a geeky 20-30 something Asian Doctor would also be really cool.