Speaking in general, the TV series (both runs, plus the 1996 Doctor Who movie) are the true "primary" continuity.
The "Doctor Who" comics strip that ran in Great Britain in the 1960's in Radio News is clearly a different continuity, and it did not feature the same companions as the TV series (noting that, until the end of the Second Doctor's televised adventures, his companions basically had overlapping tenures, and there was no obvious point where he would have been having adventures without them).
The "Daleks" strips and movies from the same period were likewise separate from the TV series, as the Daleks weren't owned by the BBC. And, of course, the two full-length "Doctor Who" movies from the 60s are at best loosely based on concepts and stories form the TV series, and happens to have some characters with similar names.
From the 3rd Doctor on through the end of the original series, there were various related adventures including:
- a few audio-only adventures (The Paradise of Death, featuring the Third Doctor and Sarah Jane)
- one attempted spin-off: K9 and Company, featuring the third version of K9 (the first left with Leela, the second with Romana) and Sarah Jane Smith; this was done by the TV series production team
- The comic appearing in Doctor Who Weekly/Monthly/Magazine.
The comic took some elements and characters from the TV show, but initially did not take the companions: in early story the Doctor was traveling alone, or had a companion that only appeared there (mostly notably Frobisher, a shape-shifter most often seen as (and for a while stuck in the form of) a talking penguin. Eventually, companions from the show were brought in at times at least. While based on the show, the influence was entirely one way; I can't think of any characters originating the comic that made it to the show.
Past the end of the original series, things changed a little. In theory, the Virgin and BBC books were official canon (inasmuch as anything is). The audios picked up on the first companion created in the books, Bernice Summerfield, and may have used some of the later companions, but especially once the Seventh Doctor adventures turned into the Eighth Doctor adventures, the books, the audios, and the DWM comics tended to move ahead separately.
During the hiatus between the original and current seasons, the books perhaps best mimicked the TV show. However, with a new book generally released every month, the status of the books' companions changed relatively frequently, and I doubt that the audio and comic teams wanted to try to keep up with that. While I'm sure there was some overlap in audiences, it wouldn't have been complete, and having to explain a companion change as frequently as was done in the books would hamper the story-telling in the audios and comics, neither of which had as much room for such as a full-length novel.
Again, in theory, when the new series started, I think most readers of the books assumed that whatever happened there had actually happened in the show's continuity as well. Since a number of the authors of books were involved in the writing and production of the show, this seemed reasonable - up until one of the Seventh Doctor novels was adapted as a two-part Tenth Doctor story (by the novel's author, Paul Cornell; the novel Human Nature became the "Human Nature"/"The Family of Blood" two-parter.
Logically, since it's not particularly reasonable to assume the exact same events happened to the Doctor twice, this pretty much means that the novel could no longer be considered as part of the Seventh Doctor's continuity, which tended to mean that the entirety of the novel run could no longer be assumed to be part of the TV shows' continuity.
In essence, it's the same thing that happened with the Star Wars continuity. When there was no expectation of significant stories moving forward from Return of the Jedi, the books and comics being produced were considered official canon; once an opportunity arose to revive the "franchise" in its original medium, that basically got thrown out the window, since the prospective audience of people to come see The Force Awakens was much broader than the audience of people who would know what had happened in the books and comics, and since some changes (like the death of Chewbacca) didn't make much sense when returning to a visual medium (where he's a character that just requires a tall actor will to where a suit, or can be done via CGI if required, who is instantly recognizable, and (due to the suit) not necessarily subject to being 40 years old than in the first movie.
But, I digress....
The comics and audio adventures have been a way to create new stories about not just the current Doctor, but previous regenerations as well. Actors whose appearance doesn't match up with how the character looked when that regeneration was last seen can still be involved in audios; plus, as some of the actors involved are getting rather old, the format allows an adventure story without the need for stunts, make-up, etc.
Looping back to what I said first, the TV series is still the primary continuity, and most of the secondary material uses that as its jumping off point. Very little comes back into the TV series, and there's hardly any crossover between the audios and the comics (for example).
Personally, if you enjoy the new series, I would explore outward from there and just discover what you like. I would encourage checking out the original series, if you haven't, and trying books about the incarnations of the character (and the groups of companions) you've most enjoyed in the past.
From there, look more closely at the items you've enjoyed the most, and look for other Doctor Who work by those creators. Or, at least, if you found something that you really didn't like, stay away from that creative team.
For the novels, keep in mind that the hiatus continuity runs through something like 130-140 novels (50+ with the Seventh Doctor, and around 80 with the Eighth Doctor). There is a definite continuity in place there, and one novel may well refer to events in a previous novel. You won't necessarily be completely lost if you skip around, but it may be somewhat confusing at times. Some stretches pretty much need to be read in order. Note: Novels about previous incarnations (including BBC books about the Seventh Doctor) are much less interconnected, as are the novels about the Ninth Doctor onward.