What you choose to write depends on how you want to capture yourself. You can start with the basic stuff - where you were born, how many siblings you have, when your birthday is, etc., and move into the more dynamic stuff like what you want to do with your life, what kind of activities you enjoy, whether you are on any sports teams, your values and beliefs, your religious viewpoint, etc. etc.
Your introductory paragraph should engage your readers and make them want to know more about you. It should make the reader have new questions to ask you that you answer as you go along. To give you an example I've included below the first paragraph of an autobiography I wrote about myself awhile ago:
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"I am from a family of cowboys and cowgirls. I was born and raised in Thunder Bay, Ontario – a small city by national comparison, but the largest city in all of Northwestern Ontario with a population that fluctuates around 100,000 people. It is a rather isolated city closer to the Canadian border with Minnesota, USA than to its nearest domestic municipality Winnipeg, Manitoba. I have a great deal of pride in my hometown, and I feel a very close connection with my family; we have all been through a tremendous amount. I was born to a frightened teenage mother of seventeen, and a twenty-year-old father ready to accept the consequences of their mistake. Three years later my brother William was born. I wish I could say the rest is history, and that we lived happily ever after, but this is far from the case. Needless to say we all endured a tumultuous eleven-year separation until they put the final stake in their marriage and divorced when I was seventeen years old because my dad was ready to re-marry. Shortly after, my half-brother Michael was born to my father and his new wife – and the rest is history."
There are several ways to approach this. I think that I will take the second question first. In all honesty, the opening to your autobiography is going to be a challenge. On one hand, if it is too sweeping, it might be undercut by what is going to follow which is your life, sweeping to you, but might not hold as much power with readers. On the other hand, figuring out how to open a story about your life is tough because how can this really be done. It's not like your life is over, and you can only write it from the point you are at now, and so your opening statement is going to be incomplete because your life is ongoing. I have always thought that paraphrasing a line from literature with which you are familiar might be a good start. I would incorporate the author and then the line and discuss how it can be tied into your life. For example, "Dickens once wrote, 'It was the best of times, it was the worst of times,' and heaven knows that sums up my life." Another example would be the closing line from the film, "Se7en: "Ernest Hemingway once wrote 'The world is a good place and worth fighting for.' In my life, I have believed in the second part."
In terms of what needs to be included, I would think about creating a timeline from birth to where you are now in age. At each age, try to note down an important event in your life. It's fine if one year has more elements than another. If this done, this personal timeline should should encompass quite a bit, and from this, an editorial decision can be made as to what to include in your narrative.
I keep six honest serving men
(They taught me all I knew);
Their names are What and Why and When
And How and Where and Who.
It seems to me that it would be virtually impossible for anyone to start an autobiography without stating where he or she was born. So your first sentence should be easy. Just say that you were born in such and such a city in such and such a state (or country). (You don't have to say when you were born unless you want to.) The next sentence ought to follow naturally from the first. It would briefly describe what kind of home you lived in. Then it would be natural to tell what your father did for a living, and what your mother did. It would be natural to tell whether you had any brothers or sisters and to described briefly what your relatives were like.
This should get you started. Then you would want to talk about yourself. You wouldn't need to start when you were a baby, but you might start when you went to school, what the school was like, whether you like school, what subjects you liked and what subjects you disliked.
Once you get started you have gotten started. Some famous man said that once you get started the job is half done. Writing about yourself is a good way to figure out who you are, which can be a long-term project but one that is absolutely essential.
I would definitely try to avoid beginning your autobiography as if it were an encyclopedic entry. (Example: "I was born on January 1, 1995 in New York, New York to the parents of John and Mary Smith.") Nothing could be more boring or less inventive. I would probably try to begin your autobiography with a specific event that occurred during your life--preferably one of high interest that will catch the reader's attention and continue to hold it. You should eventually give a historical background about you and your family, but I would try to position it after your introductory opening.