It must be a hard gig. You have to create the character and lend him a whole new look and feel. And I don't see how you cannot be influenced by your earliest Dr experiences. He's certainly of an age to have been part of the Pertwee generation. Whereas both Matt Smith and David Tennant seem to have opted for a variation on Tom Baker, who was the most outgoing and frivolous of the earlier years Drs. I started with the 2nd Dr, Patrick Troughton's bumbling and forgetful Dr, who I enjoyed. Jon Pertwee was all business, with a hint of mischievousness, or cheekiness. And although he was only there for 4 or 5 seasons, he is the one I remember most. .
I just wonder how much input the writers have into the final character. I imagine they give a general guideline of the kind of person he is, and the actor takes it from there. Which is characterised by the mad hunt through the wardrobe with each new incarnation.
My greatest Dr Who experience was going to the cinema in the late 60's to see Ben Hur (I think) and the first flick was unannounced and turned out to be The Dalek Invasion of Earth (Pertwee). Loved it. [Those were the days. 2 movies with an intermission. But with Ben Hur, it made a long afternoon of cinema. Not complaining though :-) ]
It's always interesting to watch how they 'get into the role' in that first episode. And how the old companion deals with it.
I thought Clara was a brilliant companion, perhaps my all time favourite. And the way she sloooowly warmed to this old man after her fun filled Dr, was fun to watch.