One further point I'd add then is the show is designed, at least since 2005, with several points you can get on-board from as a neophyte to the show. The Christmas 2012 special is the most recent of these. There are two key points to each of these jump-on points:
1) The show's very long continuity is not disregarded and the newbie is aware that the Doctor has a major history to him, but the specifics of that history aren't necessarily important now; all that's important is that sense of history and a deep past.
2) The plot starts fresh with no major dangling plot threads that are required knowledge to understand the current storyline.
This also applies to the Sonic Screwdriver. In the canon, it didn't even exist until the Second Doctor invented it and not every Doctor has wanted to use it. Consequently, as its inventor, the Doctor is naturally going to repeatedly upgrade the hardware to perform ever more esoteric tasks. Even the recent arrival of the "red setting" is a long-dangling plot thread tied up. At this point the Screwdriver can be reasonably interpreted as an extension of the Doctor himself.
Maybe this is helpful?
1) The show's very long continuity is not disregarded and the newbie is aware that the Doctor has a major history to him, but the specifics of that history aren't necessarily important now; all that's important is that sense of history and a deep past.
2) The plot starts fresh with no major dangling plot threads that are required knowledge to understand the current storyline.
This also applies to the Sonic Screwdriver. In the canon, it didn't even exist until the Second Doctor invented it and not every Doctor has wanted to use it. Consequently, as its inventor, the Doctor is naturally going to repeatedly upgrade the hardware to perform ever more esoteric tasks. Even the recent arrival of the "red setting" is a long-dangling plot thread tied up. At this point the Screwdriver can be reasonably interpreted as an extension of the Doctor himself.
Maybe this is helpful?