the first 3 AC games are all connected pretty closely but after that they become self-contained stories, though the animus current day stories are all connected.
black flag is my favorite of the "old style" of AC. the story has like, little to nothing to do with anything else going on and the current day stuff is MOSTLY non-intrusive. there's some extra story to the world at large if you want to look around for it, otherwise they are like 5 minute snippets. also. the only thing better than being a pirate or a ninja, is being a ninja pirate.
i didn't play origins, but i think that's where they started to take a new direction in gameplay. i wasn't SUPER interested in playing odyssey, but i actually got a lot of hours sunk into it. the story is interesting but there's so much side quest type stuff that it's pretty easy to get distracted and then you lose the sense of intensity that the story wants you to feel.
so far i've enjoyed valhalla. played it all night and now i'm going to bed. i had one crash to desktop halfway through my first game of orlog or whatever it's called. but the game seemed to save it as a win, so when i turned it back on, i was standing in front of the guy and he was complaining about losing. /shrug
i don't know what to think about the loot system at the moment. on one hand, the odyssey system was nice and i was changing my weapons and armor out on a regular basis... on the other hand, you get so much crap in that game that sometimes you might change your gear 5 times in 10 minutes, but then just get TRASH for the next hour.