Let's be a little realistic in this post as well as in the comments so don't give me your Hiddlebatches or Cumblestons. Although, if you were about to say David Thewlis, you're right. That'd be perfect.
Here are my five choices for the Twelfth Doctor...
5. Damien Molony
He seems to be a popular choice. Not a bad look.
4. Warren Brown
Nobody's named him yet. He's up for work now, isn't he? I think he'd be a good transition with Clara as his first companion.
3. Thomas Lockyer
A change in pace with an actor of a different age. From the little I've seen him in, I think he'd bring the right blend of experience, youthfulness, and foreignness that the Doctor is known to have.
2. Ben Daniels
Much older and probably an unexpected choice but change is good, especially since this is Doctor Who. I was trying to keep away from choosing an actor with a rectangular typical hero-like jawline but the energy Daniels might bring would be worth it.
1. Lee Ingleby
My top choice is Lee Ingleby. He's unknown and, as the Doctor Who casting people look for, has performed the far ranges of personality from being hyper in Harry Potter to being straightforward and serious in MI-5.
Who do you want to pilot the Tardis?