How do I add a classical music album to my library with all the movements in order?
You need a computer to do that - either a Mac with the Music app or a PC with iTunes installed on it:
Update to the latest version of iTunes - Apple Support
Then import that album into the music library:
Import songs from CDs into Music on Mac - Apple Support
Import songs from CDs into iTunes on PC - Apple Support
And finally sync the library to your iPhone:
Sync your iPhone, iPad, or iPod using your computer - Apple Support