Where can I find a list of all of the document types in CORE and infoAdvantage?

You will want to enter DTYP in the Jump to field in CORE to see a list of document types. There you will also see the document type name, category, and category name. (Note: You will need ALL_READ access to be able see this. If you don't have ALL_READ access, you may enter DCTRL in the Jump to field instead).

To see what document types are in infoAdvantage, you can choose a report like GA-999 and refresh the list on the document code to get a full list of the all the document types.