Is there an accepted order in which "List of"s should appear in the document?
For example, I have a section dedicated to "List of (Code) Listings", another for "List of Figures", and another for "List of Symbols". Is there a preferred order in which these should appear in the document?
No.
But you can look at other books and see if there is a common pattern.
I would put them either alphabetically or else by size or perhaps importance. But put all the lists together in the TOC not interspersed with other things.
In academic writing, lists should appear at the end of the document, just before any appendices.
In fiction, a single list of characters might appear after the table of contents and before the first chapter. Additional lists appear at the end of the tale or volume.
Hope this helps.
The only rule I have seen is do not make "List of One Thing" where your list (and sub-list) only have one componant. If you have Item A.1 then you must have an A.2.
