You can control whether an app shows all notification content, hides sensitive notification content, or doesn't show notifications at all on the lock screen by going to Settings > Apps & notifications > See all apps > [App name here] > Notifications > On lock screen (apps which support Notification Channels will make you drill one level deeper to apply that option per-channel instead of per-app). The only way to display certain notifications on the lock screen but no others would be to edit the notification settings for every app - disabling notifications at Settings > Security & location > Lock screen preferences overrides any per-app configurations. I definitely see how that could be improved so I'd encourage you to use Settings > System > About phone > Send feedback about this device to share your thoughts with the developers.

And I'm afraid I can't recommend any third-party lock screens. While Android provides ways for apps to replace the launcher or default messaging app it does not make a provision for swapping out lock screens. This means that all third-party lock screens run alongside the default one and that often results in a somewhat hacky experience where things don't always work quite right.