Is the only way to download music to my Mac and iPhone through Apple Music for $10.99 per month?

The Music app on macOS can rip from CD media, and can import audio from any source.

Here is how to use the Music app on macOS:

… Apple Music User Guide for Mac - Apple Support

See the section “Get music from other sources” in that document.

Here is how to sync macOS with an iPhone or iPad:

… Use the Finder to sync your iPhone, iPad, or iPod with your computer - Apple Support

Confusingly, Apple has a couple of different Apple Music apps including the one for macOS, and has an Apple Music subscription (music rental) service. They overlap in some parts, but are different. And yet more confusingly, the Apple Music service can sync music from other sources: Use Sync Library to access your music library across your devices - Apple Support. And yet further confusingly, there’s a completely separate service called iTunes Match, which allows you to sync music using iCloud (without Apple Music) and to get better recordings where available—and AFAIK, an Apple Music subscription includes the equivalent of iTunes Match, and as mentioned does include the music sync capabilities for your non-rented music, too.

PS: If you do use Apple Music to sync and it gets confused:

… If songs are missing from your music library after you turn on Sync Library - Apple Support

No. A subscription is not required.

If you wish to purchase tracks for download, you may do so at the iTunes Store by following the steps in here Buy music from the iTunes Store - Apple Support , or from any other download retailer such as Amazon or Bandcamp.