Download the latest version of the Google Play store which has been released just now which comes with the version number as v12.2.13 and brought the most recent definitions of Google Play to protect and also more refinements regarding the new design that we have seen since a more than a couple of months now. Such as the apps slide-show preview is now shown, the background is more white and minimalistic, and the description section of the app has been updated.
The Download link for the latest Google Play store 12.2.13 is given below from APK mirror which is a reputable website when it comes to downloading genuine android APK. Along with that, you also get the latest version of the Google Play services which is the core component in function of all your Google apps and so ignoring the play services updates is not a good idea.
Note that the newest version of the play store is stable, while the play services latest version is still in beta stage. Links for both the APKs are given below. And make sure before hitting the install button, you enable the unknown sources option from the Settings > Security and scroll down until you see it, then you can smoothly install any apk downloaded from the internet.