Re: Stories we would like to see...
For me the most underused aspect is Time itself - one of the more interesting stories was when rose went back to the past to see her dad, or with the Sally sparrow episode where her friend was instantly ported back to the turn of the century - ignoring the rest of the plot its the aspect of the show thats rarely exploited - the tardis travels through time.
So My Basic plot line would revolve around a time chase.
Think Cardiff 2007 and a man disspears in an alley leaving just his clothes behind - 2107 the exact same corner a naked man shuffles accross the street and breaks into the cloths store.
Switch to the doctor who's just noticed a little blinking light on his console and looses his smile and leaps frantically on the TARDIS controls, as he bursts out of the TARDIS he sees the man staggering bent double in pain and then vanishes as the doctor gets close.
1807 Same location the man reappears in pain (think of the original apperance of kyle in the terminator here - wracked with pain - minus the glowing ball of energy)
The doctor then must chase down this flying duchman through several time periods. The device of always using the same location but modifying it for its time period is important - that people instantly recognise its the same place but theres a lot of changes - unlike other parts of the doctor series where he's traveled in time this little trick would really bring the time travel home to people as they can see how much a location can change... the traveler can go from roman times, where the city was nothing more than a field to the far future where its a megatropolis.
The story is about an experiment of the Timelords, the man was experimented on and basically left to fall through time. This can demonstrait the very cold nature of the timelords as they just didnt care about the man and left him be - forgotten like he just didnt matter - as it turns out we know who the architect of the experiment was and this is yet another part of his dark past we find he needs to attone for (they dont call him the "doctor" for nothing") showing again just what a very bad man the doctor was like without a human assistant.
The man himself hates time itself by this point - since each time he shifts through time he cannot take anything with him he lives like the lowest beggar. There should be a scean where the Doc's assistant talks to the man - him hating the doctor for what he's done, making the assistant see the doctor in a new and disturbing light, but the embittened traveler should be shown to explaon to the assistant that the doctor needs them and never leave them
Ultimately we get to the climax where the doctor cannot fix the mans time shifts, but what he can do is excellerate the time shifts so effectively the man just vanishes in time never to reappear, becoming part of the fabric of time itself - effectively ending the mans "life"...
We now humanise the Doctor as he's faced with the choice of leaving the poor soul to randomly fall through time always living like a wretch - but Living.... or ending his pain. The choice is then left up to the assitant to make - the traveler offers her the choice to make which in effect is offering us the choice - the show ending before the assistant actually makes the choice so we leave it making us wonder what we would choose.