I would really like to style my category widget in the sidebar beyond what the theme control panels offers.
Specifically, I would like to give each category and subcategory item a background color and borders on both sides that change on rollover...basically styling them like buttons.

Well I figured it out. Using the Firebug extension for Firefox, I figured out what CSS selector to add to the inserts box to target the categories widget. On mine the one that worked was:

#right #categories-381603721 .widget-content li.cat-item{}

I had to get more and more specific, and it finally worked when I added the #right selector.

I am using Category Order plugin in my Wordpress installation, so your CSS selector(s) for this may be different. But the key for me was getting more specific and adding selectors for it to work.

If you don't use Firebug already, you absolutely must start! It is an indispensable tool for looking into the structure of a page and figuring what css rules are being applied to any element. Once you have it installed you can right click on any element in a page and choose "Inspect Element" and it will show you that element in the source code. Good stuff!

Is Category Order working for you? I can't get it to work with Atahualpa. My categories are sorted either by ID or name, per the theme's options. I need them sorted differently but so far I have not found a plugin that will over-ride the theme's settings.

Thanks for the styling tip.

Yes, Category Order seems to work fine for me.