The correct answer to setting a default is not this. See http://www.libre-software.net/change-the-default-application-ubuntu-linux
titled "How to change the default application for a given type of file in Ubuntu Linux" for example. Basically, right-click and there will be a "Properties" menu. There's a button called "Set as default" under the "Open With" menu there. Unfortunately, the programs I've installed that I'm not looking for (PDFshuffler or PDFsam) aren't showing up, so I'll have to figure out another way. For those who are looking into getting more programs to show up on the list of applications, you might want to consult the thread over at viewtopic.php?f=47&t=103669
("Can't set Adobe Reader as default application") which suggestions changing the file in usr/share/applications somehow.
EDIT: I figured this out. LInux Mint Cinammon (or perhaps Nautilus is to blame) HIDES FILE EXTESIONS like .desktop. So if you go to /usr/share/applications and see a bunch of filenames without a .desktop on them, and you try to open one with gedit, it won't open. You hve to append the .desktop to it. Once you do that, you follow the directions in the above noted thread: 'Find the line that says "Exec=acroread" and change it to "Exec=acroread %f"'. Change the acroread to match the program you're fixing. Quite frustrating that Cinammon/Nautilus does this.
As in many cases (in my limited experience 6 month or so experience), KDE is superior. If you go to System Settings, you'll find under the "Common Appearance and Behavior" menu a "File Associations" section which will handle this (haven't tested it yet). Confusingly, there's also a "Default Applications" section under the "Workspace Appearance.." menu, but that doesn't seem to hit what you and I want.