Do I need to begin from the first game for the story of Assassin's Creed?

This is matter of player opinion. There is a story in Assassins Creed which involves a person in experiment where scientist inspect human dna and get's back into the history seeings the events by itself. If you just want to enjoy the gameplay mechanics and the story which happens in actual gameplay, you can just start any series. But if you want to know the other story which happens behind the "curtains" you need to start from part 1.

This is a complex question to answer because of the series' approach to story telling.

Short answer

In my considered opinion:

• By not playing the earlier games you will miss out on some of the story.
• The story that you miss out on doesn't matter.

Long answer

Each game tells two stories - one set in modern times, one set in a particular period in history. The series' central conceit involves the characters in the modern day using technology to explore the memories of their ancestors in virtual environments, as part of a secret war between two factions (The Assasins and the Knights Templar) which has been going on for hundreds of years.

In each game there's one main story arc told from the perspective of the ancestor whose memories are being explored, set in the time and place they lived. The majority of the gameplay happens from this perspective. While some the characters in these games do cross over (most notably, Ezio Auditore is the primary protagonist for the historic parts of AC2, Brotherhood and Revelations), the relevant parts of the narrative tend to be largely self-contained, and can be enjoyed without the context of the rest of the series.

Meanwhile, the story of the modern day characters begins in AC1 and is progressed by each game in the series. It largely seek to justify the reasons for exploring the memories of the character in the historic parts of the game, and usually there will be some sections of gameplay where you'll need to control characters in this story in order to progress. To follow this plot from the beginning you'll need to start from the beginning of the series.

In my opinion then... the modern day story is pretty crazy, starting with megacorporations and conspiracy theories, and quickly moving on to ancient alien races and beyond. The games in the series do try to summarise the story so far for new players, but whether they succeed is debatable. However, the game will tell you what you need to do to advance the modern day part of the story even if you may not fully understand why you need to do it, and since the majority of any given game will be spent in the historic setting anyway, it's debatable whether missing parts of the story will effect your overall enjoyment of the game.