from my experience, installing the framework and Play Store APKs won't work. it will attempt to load then force close on you,
the only way i have succeeded in making Play Store work (say i deleted it--stupid mistake) was to flash a different recovery tool (such as Clockworkmod Recovery after rooting the device) and getting Gapps.zip from somewhere, then booting into Clockworkmod and flashing the gapps.zip file by choosing 'install zip from sdcard' and browse to the folder you placed it in on the card. then you should have Play Store and things like Gmail and other apps installed and working.
Samsung Galaxy S3 (Stock, rooted TouchWiz)
Samsung Galaxy Tab 3 7.0 (non-rooted, stock)
Samsung Galaxy Tab 2 10.1 (obsolete, slow, rooted)
Samsung Galaxy Note 10.1 2014 Edition