I've reread the tutorial message that's displayed at the beginning of it, and I've tried to find an explanation online, but there's been no such luck. What do you do with the guns/money/other valuables? The game says to report it to higher office or something, and there's an achievement for having the money "in the trunk", but I haven't found a way to do either.

You've probably found an answer elsewhere since, but in case anyone else comes by this post, maybe via google like I did, I will provide the answer.

There are two achievements for the game: Cleaning up everything and getting all the money.

So, all the paper money you find, dump that into the blue lock box that belongs to the janitor. Everything else goes into the incinerator.