The µg project has made good progress. It is now possible to use GMS Core, which makes it possible to use the Google Cloud Messaging push service (which is e.g. useful for the alternative messenger Threema).
The installation instructions can be found here:
Note that you have to install Xposed and an Xposed module to run GMS Core. Moreover, you have to deinstall the NOGAPPS Maps API (see http://forum.xda-developers.com/showpost.php?p=62034536&postcount=1108 ) because GMS Core provides this functionality, too. I have however not tested it, and it may not work properly yet on GMS Core.
For the installation of BlankStore, I can recommend the Sysfile Copymaster (see https://play.google.com/store/apps/details?id=com.flextrick.sysfilecm - downloadable via the apk downloader). You can then install the Blankstore without having to (re)mount the system partition.
One user has posted an overview of the NOGAPPS project: https://fralef.me/using-android-without-google-apps.html .
Finally, the newest build of GMS core seems to be stable, but older builds had bugs where the CPU activity spiked. It is of course possible that you will encounter other bugs, too. Still, I am satisfied by the current version.