I like to use this: GooglePlayDownloader
Though I had to edit the source code to get it to work for me.
You can browse the play store from your pc and also search for any updates to your apk's you have downloaded. I then adb install the apk's I downloaded.
I run it under linux but it is written in python so should be cross platform.
As said in your comments you use your google account but this software is local and not on a web server. Plus it is open source so you can trust in what your account is being used for.
You will need:
- Google Email
- Google Password
- Android ID
- Laguage Code (example: en_US)
You may also be interested in a project called microG. It mocks the gapps but doesn't actually provide any functionality.