I'm fairly certain a comedy actor doesn't qualify as a comedian. Most actors have appeared in comedy roles at some point in their career - I don't consider Robert De Niro a comedian for example.
Sylvester McCoy was voted best Doctor whilst he was the current Doctor (as was David Tennant twice) - the only three years that Tom Baker didn't win it (he came second on all three).
Not forgetting William Hartnell.
Usually the first actor to play a role in a TV series/series of films are the most fondly remembered, but this never seems the case with William Hartnell. I watched "The Gunfighters" the other day, and while the episode was mostly awful, Hartnell was still good in it, even though he was apparently quite ill by that time and kept forgetting his lines.
I think the key to a good Doctor is for an actor to be cast that can do drama and comedy equally well (there was almost no comedy at all in Hartnell's Doctor). The three who tend to be the most popular (Tom Baker, Patrick Troughton and David Tennant) can do this.