Just use Evolution
sudo apt-get install evolution
It has seamless integration with google services (email, calendar via caldav and contacts via carddav) and even exchange web services (if you use outlook.com or some corporate exchange server). Just setup your gmail account and your done.
If you want to use the account plugin backend you need to install the gnome calendar app to get access to google calendar, gnome contacts and for email you can use whatever you want with imap. If you use this method you need to setup your google account in online accounts prior to use these apps.
Best bet it to use evolution route.