What is the most drupally way to add a slide show (as a block? So I can reuse it in multiple places) I'm very new to Drupal 7, and just getting started.  

I'm looking to add this slide show on my site:
http://jquery.malsup.com/cycle/int2.html

The "Manual and Auto Advance
(hover to pause, click to advance)" one.

What is the best way to do this?  My understanding is that Drupal 7 already supports a lot of core jquery stuff.  So, in which drupal file would I add the code

$('#id_name').cycle({
    fx:     'fade',
    speed:   300,
    timeout: 3000,
    next:   '#s3',
    pause:   1
});


If this plugin is not already supported, then in which drupal file would I add the jquery cycle declaration, and where would I install those files?

More importantly, I am asking these operating under the assumption that I should make this a block, so that I could conceivably show this slideshow in multiple places on my site.  Is that a good strategy, or is there something better?
If the content you want to use is already in nodes then you could use Views and Views Slideshow (which uses the cylce plugin you linked to).

With views you can create a block which can be re-used wherever you want in the site.

Learning how to use Views is one of the best things a new user to Drupal can do, it'll provides a lot of nice tools in a point and click interface.