What was the Mac that Ran 'System 1'
Wikipedia to the rescue, they even have an article dedicated to System 1:


  System 1, also known as Macintosh System Software was the original Macintosh operating system. It is a part of the Classic Mac OS family, and ran on the Motorola 68000 microprocessor. It was released on January 24, 1984 along with the original Macintosh and was replaced by System 1.1 on May 5, 1984.


and a lot more about all other releases.