Sorry about the delay, Cait. (I missed the email notification for your reply.)
KB937287
... Odd. That's an update to the Vista Installer system. (It's supposed to be a prerequisite for your Service pack 1 for Vista.)
Let's have a go at that one first. Rather than using Windows Update, let's try getting that via the KB937287 installer download available in the following Microsoft article:
[A software update is available for the Windows Vista installation software feature|http://support.microsoft.com/kb/937287]
Does that update seem to go through okay? If so, restart the PC and check for updates again. Are you still getting offered the KB937287?
If not, see if KB979683 will "stay installed" if you update with it now.
If those two go through, check again for any other updates that might have become available, and stock up. Then try another iTunes install. Does it go through properly this time?