iTunes 10.7 is required for installing iOS 6 or later on your devices.
You can download iTunes 10.7 from here: http://www.apple.com/itunes/download/ and install the same over your existing installation of iTunes.
Once installed you will be able to update your devices to iOS 6.0.1.
The computer is now booting properly?
iTunes 10.7 is not as a rule required for running iOS6 on older devices, just for brand new ones.
You could download iTunes 10.6.3 and install it manually. I really don't like the automatic updaters, especially on equipment that is fairly old as yours must be if it is still running Snow Leopard.
iTunes 10.6.3.25 - http://support.apple.com/kb/DL1575
Using OSX 10.6.8 you can, of course, install the newest iTunes, 10.7. Again I prefer to download it and then install it manually rather than letting an automatic updater try. Download using the iTunes tab at the top of this page.
Maybe this is old fashioned but run Disk Utility and verify first your hard drive and then if it reports okay repair your permissions before installing. If errors are reported they need to be fixed first. Repair permissions afterward too.