QGis was my introduction to all of this, and I got my self started with the material on the QGis site - http://www.qgis.org/en/documentation/manuals.html
The development of the software in recent months has left quite a lot of the third-party tutorial material behind but the changes have all been added features rather than a radical re-design so working through some of the older tutorials will give you a good grounding in the basics and prepare you to dip into the manuals when you're ready to do more adventurous stuff.
As you get more confident, its worth having a good GRASS reference to hand, like "Opensource GIS a GRASS Approach" by Neteler and Mitasova, and "PostGIS in Action" by Obe and Hsu (Manning).
And finally, its worth tracking the "Planet QGis" blog for more technical and development stuff.