Following some additional study of WordPress, it appears that what I am trying to accomplish can be done by creating a Theme.
A Theme is simply a collection of custom Template files.
A Template file is simply a modified version of the wp-content/index.php file. Templates can be created to modify the way that specific categories are displayed.
So songs can be displayed in chord/lyric format by assigning them a specific category such as “Song”, and then creating a template for that category to format the chord/lyric display (category-X.php).
Similarly, I should be able to create a category and template for the weekly song lineup.