Download Play Store version 16.9.15 or 17.1.13 for Android 4.2.2.
Since the official Google Play Store cannot be downloaded from Google's own website as an APK, you must use reputable third-party repositories: Android 4.2 2 Play Store Apk
Since the Play Store often stops self-updating on older versions, manual installation via APK is the standard workaround. Download Play Store version 16