I never read any Doctor Who novel or listened to any of the audio dramas, but I've been growing curious about them because a lot of the concepts, locales and relationships the series tries to juggle with feel like they could to be fully realized in those types of media.
One thing they can do with these audios is do stuff the BBC themselves wouldn't do in case it upset kids. There's a bit more death and destruction, more adult themes handled more fully very often and so on. It's a slightly more adult take on Doctor Who, I suppose, much like the Virgin New Adventures books that were published while the show was off the air. This sort of stuff is limited to the first 8 Doctors, though, as the license distinguishes and splits between old and new Who.
I think they're a really fantastic 'form' of the show. The books are alright as well, but are I think a bit more hit and miss. I usually listen to the audios when doing household chores and stuff - washing the car, dishes, mowing the lawn etc. Good way to pass the time.
For audios, check out
Dark Eyes. It's a wonderful place to start. Features the eighth Doctor engaged in a war between the Time Lords and Daleks (though not THAT war), the introduction of a new companion, him ditching his old costume for something more Eccleston-like, and a variety of time periods including an alien planet where the people have grown to worship the Daleks as benevolent gods. There's also lots of Time Lord meddling, with one Time Lord in particular played by the same guy who did the Dream Lord.
It's really very good. It's written by Nick Briggs, voice of the Daleks/Cybermen/Judoon/Ice Warriors/oh god everything in New Who (also doing the Dalek voices here), a man who is soaked in Who lore knowledge as much as Moffat or RTD.
Alternatively - as Dark Eyes is pretty expensive right now - you could jump on board with
Blood of the Daleks. This was the first sort of audios post new-Who - so features a new companion out of the 'Rose' cast played by the brilliant Sheridan Smith. These pair continue for four 8-part series' and two final special episodes, which then segway into Dark Eyes, which is like an RTD-to-Moffat sort of transition, I suppose. Many of the people behind it are the same, but there's a tonal shift for Dark Eyes.
Books, you could look into the
Virgin New Adventures. Seventh Doctor books published when the show was off air. A lot of New Who stuff began life here; RTD's contribution features a Tyler family living on a council estate, for instance. Human Nature is a NSA novel. There's even one novel (not by Moffat - he never did one - said it felt a bit too geeky, which famously pissed some of the writers off) where the Doctor's tomb is the TARDIS, which has begun to leak and grow bigger on the outside because it's dying... so I think Moffat read that book, once upon a time.
There's the New Who books as well, but I think they're all pretty much a bit too broad in focus/scope. They're kid/teenager friendly, but a bit too much. I've read a few, but they are simple - think the first couple of Potter books before JK realized she had an adult audience as well, for instance. I think they would've been better off doing two distinct ranges, but RTD apparently didn't want that. They're good, but just a bit slashy and simple, but Doctor Who itself is that a lot of the time... it's just different to the often very complex NSA novels that imo are an interesting 'more adult' companion to the main show. The New Series books just play by the post-2005 rules. They've started putting out ones from more adult writers in more adult covers under Moffat, but I don't really think they're much different, tonally, from the kid-friendly cover ones.
