Regardless of the cartoon, Doctor Who has a style and it has changed little in the last few decades.
The camera view should be third person with some thought out rotation features, the Doctor is the key character, if the Doctor is not on the screen then it just wouldn't work, FPS for instance is a no-no.
Most of the action scenes have the cameras quite high up - if you had to show Doc and Rose for instance running from a building that's about to blow up, you should put the camera on the ceiling of a corridor and pan up as they run past. This is probably due to BBC budget constraints, meaning they are more likely to use real buildings with less available space, so if the camera has to go somewhere special, it tends to be the ceiling to keep filming easy and on time.
Having the Doctor interact with stuff is vital, and the best way to do that is in 3rd person - for one thing the areas where the player would otherwise demand to see could be hidden - I mean if you should the doctor frantically typing on a keyboard then should HAH! and stepping back - well that's all your really need to do - you just need that frantic typing, maybe have some side animations (looking around puzzled for instance). Because you will have such control over the camera you can do that. Now on the other hand if you tried a stunt like that in a FPS game you just wouldn't get away with it - you'd have to make those fingers type properly. It's such a vast difference in technological concern, but the main thing is that I think 3rd person view is a no brainer - people need to see the (a) doctor and if you can show some mannerisms then fans will love it.
Remember that Dr.Who has a long standing, you might be trying to please a massive fan base with different attitudes, like whether hoping that Tom Baker will return as the doc is a possibility, or do we think Rose is a bit of a slapper, doesn't matter what you look like, just so long as your the doctor

- I wonder if that's why they got a 12 year old doctor this time...
I digress...
Yeah, try and concentrate on what makes Dr.Who what it is, it's all in the Doc's personality, capture some of that and you can't go far wrong. Ohh and the main enemy should always be a Dalek, Cybermen are much less threatening but would also make for a cool enemy.