I've been using Copperhead OS for a while now, and Google Play Services (aka Google Mobile Services) free for a lot longer. Today somebody was talking about getting apps not part of F-Droid, their method involved downloading the apk files manually from a website.
I think my solution is better, but it requires another Android device. This extra device is one I keep locally, with minimal usage. It has the Google Play Store along with F-Droid. So I buy my apps through that device but then I use a feature in F-Droid called "Swap Apps."
This creates a repo that other F-Droid clients (on the same LAN) can use and download from. So my other devices then download from that repo, not requiring Google Play Services or downloading apk files from the web and forgetting to update them.
Ideally all apps should be received through F-Droid, however this isn't always possible, such as SeriesGuide where it can't be included because of API keys. Now that SeriesGuide is on IzzyOnDroid F-Droid Repository I get it there, but SeriesGuide X from the Google Play Store.
It's still import to note that apps such as Pocket Casts and Action Launcher 3 can't go though this system, or any as they have licence checks that don't work on FOSS devices.