Right way to restart Oracle 12c Server with pluggable databases
I want to propose my findings as an answer. I have tested these procedures and they seem to work fine. 

NOTE: The whole experiment was done on Windows Server 2012 R2, however based on my readings I would say most of it applies to Linux too.

Shutdown


Shutdown the Oracle Database Instance to ensure that everything close cleanly
https://docs.oracle.com/database/121/ADMQS/instance.htm#ADMQS052
http://www.dummies.com/how-to/content/how-to-stop-an-oracle-12c-database.html
Shutdown Windows Server


Restart


Start Windows Server
Start the Listener
https://docs.oracle.com/database/121/ADMQS/network.htm#ADMQS044
Start the Database instance
https://docs.oracle.com/database/121/ADMQS/instance.htm#ADMQS052


Remarks

Restarting the Windows Server should do everything automatically but there are a couple of remarks.


Starting the Oracle Services on windows is not the same as starting the database instance. However they are configured by default to behave that way. Oracle Administration Assistant for Windows can be used to determine what exactly happens with the database instance when the Oracle Services are restarted. 
https://docs.oracle.com/database/121/NTQRF/admin.htm#i1006074
Linux can also be configured to start the Oracle Database automatically using scripts. Oracle Restart was recommend in previous versions to accomplish this but is now deprecated.
https://docs.oracle.com/database/121/UNXAR/strt_stp.htm#UNXAR150
http://docs.oracle.com/database/121/ADMIN/restart.htm#ADMIN12708
This step is no longer necessary, see below: If a pluggable database was configured during installation it should be manually started after restarting the oracle services.
https://web.archive.org/web/20180911225755/http://blog.contractoracle.com:80/2013/06/oracle-12c-need-to-start-container-and.html


Do note: The 12.1.0.2 patchset introduced the ability to preserve the startup state of PDBs through a CDB restart. This is done using the ALTER PLUGGABLE DATABASE command with the OPEN and SAVE STATE options.
http://oracle-base.com/articles/12c/multitenant-startup-and-shutdown-cdb-and-pdb-12cr1.php