Get on the Ubuntu bandwagon. Touted as the best free open source operating system it pays to take a look. This book, Ubuntu for non-geeks 3rd edition, might be just what you need as an introduction to Ubuntu. It isn't a geeky book but instead a drawn-out, sometimes too drawn-out explaination of what Ubuntu is, how to install it, and most importantly how to use it. Plenty of well written examples will help even your Grandmother get a system up and running.
I totally recommend the operating system and the book. Even a veteran of Unix(s), I got something out of the book. Take a look at the book and a sample chapter at Ubuntu for non-geeks 3rd edition.