This can be a fun little game. Someone upthread said something about "things making sense." I like that but, of course, different people will interpret that in each their own way. Of course that's basically little different than just accepting what you like and rejecting what you don't like.
Over the years we've seen Trek play with branching timelines and alternate continuities. I can take this as a clue to reconciling some of the inconsistencies between series and films and whatever else in terms of continuity. So while everything appearing onscreen is inarguably canon I can see it as not necessarily canon in regard to another film or series.
To start, for me, TOS is gospel. That's
Star Trek. But then it starts to get murky. I don't have any problems with what we see from the Pike era in "The Menagerie," but there are some small parts of original footage in "The Cage" that I just have to ignore. Namely, those bits about Pike not being used to having women on the Bridge. There's also the bit about Spock assuming command, ordering the ship to break orbit and fire retro rockets or some such. That's where I put my hands over my ears and hum loudly.
We really know next to nothing about the Pike era aboard the
Enterprise, but Marvel Comics did have a short run series called
Star Trek: Early Voyages that had some interesting stuff in it. I like to think some of that happened in the Pike era.
Post TOS I'm really tempted to look at
Star Trek Continues as a credible continuation of TOS. Particularly when they do stories like "Lolani."
There's a lot I like in TAS, but there's also stuff there that makes me cringe. I don't like "Mudd's Passion," "More Tribbles, More Troubles" and "The Practical Joker," but there really isn't anything in them that I can justify rejecting them as not possibly happening. Same with a few TOS episodes. I really like the episode of "The Infinite Vulcan" BUT my brain freezes when we get a fifty-foot Spock clone.

I have to gloss over that one. And then I have a BIG problem with "The Counter-Clock Incident." I like the appearance of Robert and Sarah April, but the rest of the story is just too damned stupid.I can only conclude that there are chunks of TAS that went missing somehow--pieces that explained away some of the brain cramp moments.
While I enjoyed each of the films initially (in varying degrees) when they were released I now reject all but one of them as having happened in TOS' continuity. For me TMP is the only one that gels with what happened in TOS. That said I admit I have to squint a bit to reconcile some of the visual aspects of TMP with TOS. The rest of the films (TWOK-TUC) must have happened in some other somewhat familiar timeline. From this viewpoint there remains a large blank canvas as to what happened with the original TOS crew after the events of TMP. I did find some of the early Pocket Books novels interesting in terms of what some of their adventures could have been, at least broady if not in detail.
I used to completely reject TNG, but I've softened somewhat in certain regards. I can see something like TNG happening in TOS' future, particularly the first three or four seasons. That said there are details that I tend to gloss over that don't really gel for me. For the vast most part I don't think about the later seasons of TNG. I don't bother with DS9 or VOY either. Yeah, maybe something like those could have happened, but I don't really care. I just ignore it.
I also flat out reject ENT. It's canon unto itself, but for me it has nothing to do with the original continuity. It's an alternate timeline much like TWOK-TUC as well as the TNG films. And, of course, JJtrek.
If all that sounds convoluted, well, so be it.
