Thanks everyone for your help. I will get the application turn in now.
My green card show : 07/2003
OK, that's good. This means that you were about 15 years old (importantly, under 18 y.o.) at the time you became an LPR in July 2003. Assuming that at some point between the time you came to the U.S. in 2003 and the time you turned 18, you lived in the U.S. with your father, you did derive U.S. citizenship under the Child Citizenship Act.
See
http://travel.state.gov/visa/immigrants/types/types_1312.html
for details regarding the Child Citizenship Act.
So you can file N-600 and/or apply for a U.S. passport, in any order.
You'll need your birth certificate (+ translation if the original is not in English), your parents' marriage certificate (+ translation, if the original is not in English), your father's naturalization certificate, your green card, and some proof that you did reside with your father in the U.S. at some point after entering the U.S. in July 2003 and before turning 18 y.o.
For the proof of the latter, you should be able to use your high school records for 2003 and 2004.
If you submit N-600, send photocopies of these documents with your applications (do not send the originals).
If you apply for a U.S. passport directly, before getting N-600 approved, you'll need to do that in person, at a passport application center (typically at a post office or at a passport agency). There you'll need to bring both the photocopies and the originals of the above listed documents. They'll take the originals of some of these documents with the passport application (at a minimum they'll take the original of your father's citizenship certificate, and probably your birth certificate), but these originals will be returned to you when your passport application is approved.
Even if you decide to apply for a U.S. passport first, it is still a very good idea to file N-600 and get a certificate of citizenship as well.
