According to Paramount, canon is anything live-action that appeared on screen in a movie or a regular broadcast. So TAS would not be canon under this definition, but all the series and the movies are, including the latest one.
As for the purpose of canon...well, I have to back up. What's important to me about canon isn't minutia about how this thing occured on star date ____, so how could event X have happened only a month later? Or about uniform colors...or even details of the early life of various characters. I can overlook all those little inconsistences, and I can even overlook some fairly important inconsistencies.
What's important to me is that any movie or series marketed under the name Star Trek needs to fit into the recognizable Trek universe. So that, for me, is the reason for worrying about canon.
Yes, I'd like everything new to fit in with what's come before, but I know that realistically that's just not possible. You can't make 40-some years of TV shows and movies, all written and produced by different people, all made under vastly different circumstances and during vastly different times and all trying to appeal to newer audiences, fit together. So long as they kind of fit together, that's the best I can hope for. And I'm OK with that.
So that is to me what canon is for: To keep it recognizably Trekkish.
Ah, but then to argue at all about canon is to presume that a fan has the right to decide for themselves. I agree with the Paramount canon because I actually like
the tension which inconsistencies create in a work of art. Just as when with Christian-Scripture-study (I used to be intensely Catholic) I enjoyed the creativity of the mental gymnastics I had to make to cause it all to hang together non-contradictorily, so also do I find it fun to try to make the, say, "Admiral Archer" comment or Spock Prime recognizing Chris Pine as if he truly were a young William Shatner (which he isn't) all fit with what I already know about Star Trek.
One could argue that, like all myths, the stories change but there's a kernel which stays the same. In this case, it happens to be the crew, not the actors; the general story, not the specifics.
As far as a "recognizable Trek universe," to me that's a stylistic question more than anything else. I like variability as much as general consistency. For example, throughout the films and shows, the transporter has been a main feature. But look at the differences between the TOS transporter effect and the new movie: I find that interesting.
Where a stickler for "continuity" would be upset at the change, I see the (ostensibly, change-in-art-director) as a reason for investing more meaning into the show for myself, like, "How, within the Trek universe as it presents itself, could transporter technology exist in such-and-such a way NOW when it existed there in that way?" Not that those are necessarily questions worth asking, but I find asking them pleasant and fun.
Same with the ship designs.