One of the keys to successfully migrating from Server 2003 to Server 2012 R2 is knowing which workloads will and will not work on a Server Core deployment.
There are some obvious ones that you can’t run on Server Core. For example, while you can run the vast majority of SQL Server’s features on a Server Core instance, you can’t run an Exchange server instance, or run products like System Center Configuration Manager on Server Core.
A good rule of thumb is that the majority of third party applications that have a local GUI management component won’t run on server core and that any that do will be the exception rather than the rule.
Server Core on Server 2012 R2 gives you the option of also running what is known as the Minimal Server Interface. You can think of Minimal Server Interface as a half way point between Server Core and Server with a GUI. When running this middle ground, the graphical shell is removed, but the graphical management tools and infrastructure remain in place.
You can learn more about using Server Core, including how to convert between Server Core, Minimal Server Interface, and Full Server by consulting the following blog post: http://blogs.technet.com/b/keithmayer/archive/2012/10/19/improved-taste-less-filling-more-uptime-server-core-in-windows-server-2012-31-days-of-favorite-features-in-winserv-2012-part-19-of-31.aspx