As to which version of GIS Server to use, it's really your preference. If you are a Java developer you would use the Java Server; .NET if you are a .NET developer. It is up to ESRI to ensure that the Server product in any of its flavors adheres to the GeoServices standards. Depending on your environment, you may get better performance from one or the other versions of GIS Server but in the end I would call it a matter of preference.
I am betting IT will likely want to install the .NET version, as I would imagine the Server permissions would be easier to set domain names/groups through the Windows Group Policy Editor due, but unsure if that may have any effect on it. I doubt IIS will have anything to do with setting Windows domain level permissions either, as I think it is only the web server, right?
GIS Server does live in IIS, yes, but there are a number of permissions that will need to be set up during the installation process. And just as a word of caution--this is where the installation usually gets borked. At least in my nearly one-dozen installations of GIS Server it has happened nearly every time. Good luck!