Mitzvah: literally, a commandment. Figuratively: something more. Generally, a mitzvah is a good deed which is done, not specifically for God, but for the sake of a good moral decision. They are performed for Tikkun Olam – good deeds making the world a better place. Mitzvot can be different for different people though; some people have different ideas of a good deed. My particular idea of a mitzvah is largely based on justice. Regardless of opinion, some things are just good deeds, and some bad. So with that philosophy, these are the mitzvot which I would do for God and for Judaism..
One of the main themes of the Torah is that everyone should believe in God. So as a basic mitzvah to God, I will always try to remain faithful to what God represents – morality, decency, and justice - and I will try to spread that influence around the world. I will not try to force people to believe in God; that is not a good deed, but I will try to make people understand what a good society should be like. The homeless people should be helped; poverty is probably impossible to defeat but it can be minimized, and efforts to minimize it are definitely mitzvot.
Mitzvot do not have to apply to God or Judaism, and charity is such a mitzvah. However, out of the three categories of God, Judaism, and other, Judaism, the remaining category, is also important. Judaism is a code of living, a standard which must be preserved. It is really one of society’s last hopes for morality. It makes up only 0.1% of the world population, but it has a huge effect. Regardless of how impressive that is, its effect is receding in many ways, and steps must be taken to preserve Judaism. Therefore, an obligation to Judaism would be something which preserves it, for the greater good. A mitzvah to help Judaism would be mainly to educate people about it. There is a lot of anti-Semitism in the world but there is also the simple belief that Jews have horns. The anti-Semitism should be fought, to show the world the power of the Jews, but stuff like the belief about horns should be focused on too. If the people who think Jews have horns can be shown what a good Jew really is, then it would make a huge social difference.
The mitzvot I just listed were very general, but put into the context of what my obligations to God and Judaism are, this is my straight answer: I would try to never stray from good moral decisions (basically trying to be a good person), I would give charity to helpful organizations, and I would try to decrease the worldwide ignorance about Jews by correcting every false thing I find. In the end, all the mitzvot hopefully would help with Tikkun Olam, and would better society and the greater good.