How do I prevent Word from redisplaying multiple minimized open documents when opening a new document?

Try this:  Right-click on the lower taskbar (the dark band that runs across the bottom of your screen), in an empty space, not on an icon.  You should see a small window open up that gives you different options for displaying the documents you are working on.  Cascade windows is sometimes helpful if you are going back and forth between different documents.  You can drag the edges of a document so that you can see two documents at the same time.  You just need to click on one to bring it more to the  front.  Stacked windows is another option.  Then you will see all of the documents at once.  That may be what you have had selected.  Side-by-side windows is another.  Experiment with these options.  It may help you.

A newly opened document will not cause other minimized or open Word documents to come to the front. But the newly opened document will not come to the front itself, it launches as an open window. 

The easiest way to eliminate that is by using keyboard shortcuts:

To minimize all the windows and get back to the desktop:        Windows + D

To open a new word blank document                              :       CTRL + N

To open a word document from a location                       :       CTRL + O        

There's an option under Word Options / Advanced / Display, named Show all windows in the taskbar. Turning it off hides all Word icons in the taskbar but one. This way the described behavior disappears but at the same time goes the ease of restoring a minimized document.