Despite QGIS is one of most used free GIS software with a lot of tools available and lot of help on internet,
you can add another sofwares to boost his capacity like R software for statistical (geo)analysis (https://www.r-project.org/) and orfeotoolbox (https://www.orfeo-toolbox.org/) for remote sensing analysis
There are several options! QGIS (already mentioned) is probably one of the most used. Other options are GRASS-GIS (grass.osgeo.org/), WhiteBox (https://jblindsay.github.io/ghrg/Whitebox/), SAGA (http://www.saga-gis.org/en/index.html), GVSIG (http://www.gvsig.com/pt/produtos/gvsig-desktop) andTerraView (http://www.obt.inpe.br/OBT/assuntos/projetos/terralib-terraview)