@socks QGIS is a very good place to start. Big, active and supportive community. It has GRASS inside as well, and so provides a gentle way to explore it without going whole hog. (Though you will have to dedicate some synapses to understanding the project and data structure, which is truly unlike anything else.) SAGA is very interesting, especially for raster, but I've not touched it anywhere near as much as I'd like.

There are other open source unsung notables too. Ossim, Virtual Terrain Project, Whitebox GAT, and uDig spring to mind.