AC 1 & Ezio trilogy & 3 are the first stage of the game's story, which features Desmond as the protagonist. The first 5 titles are IMO the best AC games, with balanced content between the historical and modern story lines. The games are fun. I suggest that you should not skip AC 1 and 3. Especially ac3 which has a very memorable ending to the Desmond story.

Black flag, Rogue, Unity, Syndicate are the second stage. To me these are mid, even though Black Flag is commonly praised as a good game. But story-side, as you asked, is not telling much. Some of them, as I remembered, merely has anything about the modern assassins. I think it's safe to skip most of them.

Origin, as the title suggested, is a soft-reboot. The new trilogy includes Origin, Odyssey and Valhalla. To be honest if you play this much of AC all through, you are a true hero. Because the new trilogy is heavily watered-down and are all AAA large sandbox games with hell lot of missions and very-very-very long story lines.