Each moon has its own associated deity, yes. The best offering might simply to do what they've brought us here for, though...depending on whether or not you know anyone already here, it can be something of a daunting task.

I'm sure the Prismals explained to you the concept of Chroma and moonlacing, right? Finding someone you're comfortable being physically affectionate with produces a form of energy that seems to be necessary for living creatures. Since we all have a connection to one of the moons, the natives think the gods brought us here to generate Chroma after they lost the ability to produce it around two-hundred years ago.