RE: Design of 'fixed-width' websites, optimized for universal readability across all screen-size resolutions (i.e., best viewed, with no horizontal scrolling, over broadest range of both desktop/laptop & mobile-device browsers) – What is currently considered an ideal standard for 'maximum page-width' (meas. in pixels)?
If you are going to go with a fixed width approach, your best option IMO would most likely be based on your sites analytic first. If you don't have analytic's you could build toward the most commen screen size based on global internet analytics, sites like StatCounter provide fairly reliable data.
If you serve a very large amount of users and there is no clear cut/primary screen size (view port for a more modern approach), I would suggest looking into other avenue like Responsive Design. Many sites try to server to all resolutions sizes end up heading toward Responsive Design. Good article to read on A List Apart by Ethan Marcotte; if you are unsure of what Responsive Design is.
needs to work in browsers of all resolutions.
I'm thinking fixed width
are somewhat contradictions.
To work best of desktops, laptops, netbooks, tablets, smartphones, etc., what is the currently accepted best width for a fixed-width website
Well, there really isn't one, but keep in mind you're asking for something that will work on an iPhone as well as a 30" HD monitor. That's going to be tricky.
I believe mobile Safari assumes web pages, by default, will be 980px wide. So, barring no other context here, I'd say that 980px is as good as any to pick for a universal fixed-width site.
After reviewing the tips from DA01 and JeffH, I ended up with the 1140 CSS Grid System. The perk of this is that the width is "fixed", so the paragraph lengths aren't too long, however, it shrinks nicely to work with smaller resolutions.
A neat way to get an idea how things look on smaller resolutions. I develop on Firefox with the Web Developer toolbar. After getting the "Responsive Design" term in my head, I noticed under the "Resize" options, an option called "View Responsive Layouts". This option displays the current website in a series on popular mobile and tablet resolutions.