First, use our app store, this gives you access to Accrescent and Play Store.
If an app is on Accrescent, that is our primary recommended source.
If the app isn't on there, Play Store with a throwaway account if you don't want an identifiable account as some apps you may need and use may only be on there and also be the type of app to check the installer of record to make sure Play installed it.
If an app isn't on the Play Store but unavailable anywhere else, then Aurora Store is the alternative to the above, for apps such as eBay labelled as needing to pass Play Integrity on the listing but not the app itself.
Then you have apps such as Obtainium which allow you to find. discover and manage apps from outside Accrescent and the Play Store where developers list releases directly in places such as GitHub, GitLab etc this can also be used to cut out F-Droid as an app installer with all it's issues, you can use the F-Droid website as a catalogue while clicking through the source links to where developers host sources and in most cases releases. Where you get apps like AntennaPod that only publish the app on F-Droid you can paste the AntennaPod page link into Obtainium too. The app will try to install in the background where/when it can but if it doesn't work will alert you to updates being available too.