My Windows Server is running on 3gb of memory right now, and I would like to upgrade to 16gb.
However, I don't know what type of memory to buy. I know that the notches in the physical RAM are different depending on the memory type.
Is there a way in Windows Server 2012 to detect the type of memory so I get the correct one?
No, there is no way that Windows can guess what RAM is supported.
You need to consult the hardware documentation of your server for that