is it possible to have setup run the installation automatically as normal, but then sysprep and shut down so that on the next turn on it prompts for a new product key and all that stuff? It should also reset the SID. I want to make computers have automatic names as well.

I plan to set up several different PCs (different parts) so this would be helpful.

Microsoft has an OEM preinstallation kit, but nLite seems to work. Do I just have to add sysprep and a sysprep.inf file to the GUIRunOnce?

Yes you can. The necessary files need to be in the Sysprep folder at the root. So make a $OEM$\$1\Sysprep.