admit that you were in the wrong and you realize that, you did what you could to make it up and take care of the situation, and it hasnt happened again. (and it wont happen again)
just be really honest with it, but dont go on and on about it.

Prepare for the worst.

The interviewer might ask: How will you assure us that what you've done before won't happen again here?

Tell him that you recognize that it was a mistake, and that it won't happen again because you've learned a valuable lesson from your experience: that you can't get away with crime.

Truthfully.

As you said, they are going to check your criminal record. It's much better they hear it from you, with your "reasons" and feelings and remorse about it than from a cold factual police report about it, isn't it?

I'm sure that answering the questions about an arrest as honestly and truthfully as you can will make the outcome of your interview with the post office a success.

The post office may have a position somewhere. They not only are looking for clerks, mail deliverers, and mail handlers but they also need to train people to run some of their high tech canceling and sorting machines. They also need janitorial staff.

By being honest, they may go out on a limb for you with an employment opportunity.