Here are my initial investigation prep outlines for my Servants of Gaius campaign. The writing is pretty bad, and the investigation outline itself is just a rough outline of the most likely leads (each box has a corresponding entry in a location break down that gives some of the less likely leads to find in each).

I began with my basic power groups and NPCs. Basically there is a conspiracy in Aegyptus that involves the Prefect Aulus Flaccus and his secretary Apion. There was a big outbreak of violence between Jews and Greeks in Alexandra during Caligula's reign so I decided that the prefect is instigating it to use as a cover for his activities and as a way to eliminate his enemies in the province. This gets a bit involved but the quick version is the Alexandrian conspirators are working with a cult to raise Antony and Cleopatra  (with the aim of breaking away from Rome and uniting the eastern and African provinces against the Emperor)---this is a supernatural campaign and if raised they will be mummies.
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There is also a group of conspirators in Rome itself who are working to find to location of Cleopatra's tomb (supposedly a grandson of a veteran of the battle of Actium knows the real location). So the adventure starts in Rome with a murder and the outline below shows various leads the PCs might follow (again there are a lot more possibilities than this suggests and this is only the first part of the investigation itself).
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While all this is going on I have a timeline of likely events (it includes stuff that happened before the murder to I can keep things consistent). But will put that in the next post.