How can I execute a powershell script by means of group policy on a number of machines?
The script is signed and will run on the targeted machines when you right-click and select "run with powershell".
Check out this page: http://technet.microsoft.com/en-us/library/ee176949.aspx
In particular, I think you'd want to edit your machine start up GPO to run:
The path to PowerShell.exe does not change if you have v1 or v2 installed.
An alternative solution (what I did) to bginfo:
Make sure you do gpupdate /force and logoff/logon, then you should see bginfo on your desktop.