Hello Samuel:
In terms of hardware, I would say that any brand-name server released in the past couple of years is easily capable of running Adagio in a LAN deployment. In that environment, the bottlenect is often any older workstations.If the deployment is RDP, you have to pay more attention to server RAM, processors and drives; same if there are other applications running on the same server. And if there is the possibiity of 100 concurrent Adagio users as in Brian's case, you REALLY need to pay attention to those specifications.
I even have a client with 5 or 6 concurrent Adagio users successfully running on a NAS drive, which isn't even a true server.
As for Windows Server 2012, the compatibility page still only refers to Server 2008 as you pointed out. I believe that is more of an indication that Softrak hasn't been able to test thoroughly more than it is an indication of a problem. I have a client who replaced their server with one running Windows Server 2012 (they didn't ask). It's still early but I don't expect any problems. I'll bet that most Adagio dealers have at least one Windows 2012 site.