I'd say it's fine to just start playing the new one if you don't care much about the overarching story. Pretty much every game in the series tells a story on its own, and it isn't necessary to have played everything up to that point just to understand what's going on. The story can be summed up pretty quickly (spoilers): Desmond gets kidnapped, he escapes, discovers that the gods have left a message for him, he finds an ancient thing that could destroy the world, big plot twist, the planet is saved, he sacrifices himself, the end.
Plus the games starting with AC4 are going to feature completely different protagonists, and there's no word whether the story is continued at all. For all we know there isn't even a focus on it, since you'll be playing a "research assistant" or whatever. I would recommend starting again with AC1 and going down the line though. If only to see how the game improved and changed over time, there's been a ton of new mechanics and weapons added since the first one, and I personally enjoyed every game in the series. Minus Brotherhood, it was terrible.