You can download Google Play Store app to your computer using APK downloader .... you can either copy and paste app link and get download link from APK site or install the APK downloader Chrome extension on Google Chrome.....

Here is the link APK Downloader [Latest] Download Directly | Chrome Extension v2.1.2 (Evozi Official) to APK downloader, just follow the instruction there to install Chrome extension , so that you won't have to copy and paste the app link each time you download an app...