I am still new to GR but does GRAW and GRAW 2 run on vista?

They work on my Vista home premium 32-bit.
Don't buy GRAW(1) if you want Online-action. For that, GRAW2 is a better choice.
Latest patch for GRAW(1) is v1.35
Latest version/Patch for GRAW2 is v1.05 Download these patches at ubi.com
(or ghostrecon.net or so..)
You need the latest version to join online.
Just download the latest, not all others.