Upgrade from non-server to server?
OS X Server, from OS X Lion onwards, is just another app you buy from the Mac App Store and install. You do not need to do a fresh install of the OS. There are generally no special hardware requirements for OS X Server compared to the client edition either.

To move from OS X Mountain Lion client to OS X Mavericks server, you would first have to upgrade to OS X Mavericks client, then buy and install the Server App from the Mac App Store.

The General Requirements section on OS X Server Technical Specifications page currently states:  


  
  Mac computer running Mountain Lion.
  2GB of memory.
  10GB of available disk space; some features require additional disk space.
  Some features require an Apple ID; terms apply.
  Some features require a compatible Internet service provider; fees may apply.
  Some features are not available in all countries.