Do I need BOTH jQuery wrappers or just one?
does the first jQuery wrapper (Code-Wrapper #1) include the Document-Ready function or not (Code-Wrapper #2).


No it doesn't.


  Do I have to wrap the jQuery in BOTH wrappers?


If you need DOM ready, yes you do, but in Drupal 7, they suggested Drupal.behaviors. See https://www.drupal.org/node/756722#behaviors