Aurora is a FOSS Play Store client that does not require a Google Account to download directly from Play Store. However you can login with your Google Account to download your already paid apps!
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Pros
Pro Anonymous login
Get apps directly from Google Play Store without using a Google Account.
Pro Free & Open source
Aurora Store is 100% free & open source. No ads, no tracking.
Pro Elegant UI
Interface is very nice.
Pro Works on Android TV
Pro Easy to use
Pro Spoof country or language
Get country or language restricted apps anyways.
Pro Spoof your device
When your phone supposedly doesn't work with this app you can spoof your phone as another device and download it anyway, often the app works as intended.
Pro See app statistics
Can view general privacy-related usage of the app eg. contains apps, uses GPS, etc.
Pro Option keep or delete APK file after installation
Cons
Con Violates Google Play TOS
Violates §3.3 of Google Play Terms of Service, which can lead to an account ban if you use with your regular Google account.