I have 2 desks in my office, both with multiple screen layouts. Your question made me think about how I use them and it comes down to the task I am performing.
Like others, when I am programming I typically have an IDE where I am doing work on one and a reference open on another. When doing web development my third monitor usually has a browser where I can immediately refresh my work to see results, for other development it may be a virtual machine or remote desktop that I am logged into.
When I am doing academic work, I often have EndNote (reference manager) on one monitor, the document I am writing on another and the documents I am finding / reading on the third.
Since both my desks are next to each other, I often “borrow” a monitor from the other setup to keep communication windows open (Skype, Lync, Hangouts, #Slack etc.) This allows me to keep in touch with coworkers and colleagues without having to flip windows every time I get a message.
So I would say there are three purposes identified:
Active Work
Reference Material
Communication
With your background in web development have you read things like Krug’s Don’t Make Me Think and William’s The Non-Designer’s Design Book? These are focused more on the design aspect of web however they contain some good underlying principles for data visualization as well.
Tufte’s book are all great for underlying principles even though, as you noted, they aren’t focused on modern technologies. Beautiful Evidence from 2006 has some updated thoughts but he still borrows heavily from his earlier books.
For general multimedia concepts, Mayer’s Multimedia Learning is good from a human learning perspective (my background).
I found Data Points: Visualization That Means Something to be a good modern guide.
From my perspective, I am glad you are looking down the road and recognizing that after the data are analyzed the analysis must be communicated.