What is the right order when using \frontmatter, \tableofcontents, \mainmatter, \part, \chapter, \backmatter, \appendix etc?

Prenote: as my answer expands David Hammens's one, read his answer first.

There's only one subject area with a hard-and-fast rule: front-/main-/backmatter and appendix. To recap the behaviour of the standard book class:

• \frontmatter turns off chapter numbering and uses roman numerals for page numbers;

• \mainmatter turns on chapter numbering, resets page numbering and uses arabic numerals for page numbers;

• \appendix resets chapter numbering, uses letters for chapter numbers and doesn't fiddle with page numbering;

• \backmatter turns off chapter numbering and doesn't fiddle with page numbering.

The hard-and-fast rule: Don't use \appendix after \backmatter, because chapter numbering has already been turned off by \backmatter.

(Note: Probably because Leslie Lamport didn't anticipate sections in \frontmatter and \backmatter, the standard book class doesn't turn off section numbering there.)

Front-/main-/backmatter and appendix influence the numbering of chapters, but aren't chapters themselves. (You may treat them as parts and fiddle with the \part command.) On the other hand, things like the table of contents, the bibliography, the index etc. normally are represented as (unnumbered) chapters. David Hammen has already given a comprehensive answer, so I'll add my suggestions mainly on topics where David was silent (or where I disagree with him):

• Information about ISBN, edition, copyright etc. is often placed at the back of the title page, i.e. on p. 4 of a book. (Page 1 contains the half-title, p. 2 is empty, p. 3 contains the title.)

• A dedication and/or a motto is often placed after the information page.

• For the lists of figures/tables/custom floats there are two placement options: a) immediately after the table of contents b) (if they are really bulky) somewhere in the backmatter.

• Information about the "target audience" is (in my opinion) well suited as part of a "Preface" chapter (which should be placed immediately before the "Introduction" and the \mainmatter chapters).

• For the appendix and the backmatter, I suggest the following rule of thumb: Chapters containing additional (but subordinate) information should be placed before chapters that only serve as registers. In particular, the bibliography should always be placed after "supplemental" appendix chapters.

• In the majority of books I know, the index comes last.

I'll start small and build up.

Personal preference: I generally prefer \input over \include. Chasing down blank pages because you happened to \include a file that should only have been \input can be a pain. OTOH, if the \input file starts with \chapter and you have set things up so that chapters start on a new page (or a new even page), using \input instead of \include is a 'no harm no foul' kind of difference.

Front matter:

• The title page is of course first.
• Dedications and "about the xxx": Pick up some books and you will see that the order of these varies. This is a personal preference item. Do what makes sense to you.
• You missed an abstract or executive summary, one or the other (and sometimes both) of which are often present in technical reports.
• Table of contents is almost inevitably after the dedications, "about the xxx", abstract, executive summary, etc. but before the "list of xxx".
• List of figures is usually before list of tables.

Main matter is the bulk of the book/article/whatever but the easiest to specify. Just like you have it. Just be consistent. Example: Don't switch from sections as the highest level entity to parts later on.

Back matter:

• You use \appendix before you use any sectioning commands that pertain to appendices. You may or may not want to use the appendix package. Do not use the appendix package if your document has parts.
• The bibliography typically goes before any appendices except when the appendices themselves contain citations. Then the bibliography goes after the appendices.
• The order of indices and bibliography (one, not many) varies considerably from book to book, and from publisher to publisher.

If you are not self-publishing, your publisher will almost certainly have their own ideas/rules on the right way to do things. Keep your content well-separated so that when the publisher asks you to rearrange your content it only takes five minutes to do so as opposed to five weeks.

I'd recommend reading memdesign.pdf, Chapter 2, "The Parts of a Book". It's not too big for a first look (~12 pages).

Who knows, it may even turn you into a memoir fan.

And, of course, there's absolutely no need for you to restrict yourself to Chapter 2.

If you're really interested, then I can also recommend Bringhurst.