I was hunting around for a simple method of customizing fonts on this site and came across Easy Google Fonts. This literally lets you create sets of CSS tags to apply custom Google fonts as well as system and theme fonts. Just create a font set, then set all of the available properties via your theme customizer’s new “Typography” setting.
Please note as of May 2024 this plugin appears to be abandoned.
Be very wary of using any plugin that is not actively maintained as it can lead to any number of possible security vulnerabilities.
Check out this post for a modern alternative to Easy Google Fonts.