Breaking non-critical areas of the station, littering, etc. Only go for these sorts of crimes if you are bored.
Actual Crimes
Your Job
Breaking and entering, assault, theft, murder, like actual crimes you know. This is the bread and butter of who you'll be arresting so don't feel like you're breaking the rules if they get really whiny about being brigged.
Treason
Also Your Job
Basically people who you know are traitors. These are basically at your mercy since you can either kill them or arrest them and take all of their contraband.
Weird Antagonists
Do Whatever
Who gives a shit about these, either go and kill them or let the crew kill them, whatever, they have no rights.