Your school may have academic licenses of ArcGIS available, or may have it installed in a lab for student use. ESRI offers a free 60 day trial of the software at that link, if needed. ArcGIS is able to handle most spatial analysis and visualization tasks, although you may have to add certain plugins depending on your specific needs.
If you have to publish results on a web map, ArcGIS Online is a great choice. It offers a free personal account that allows you to store up to 2GB and share your maps with specific people, e.g. your professors. With it, you don't have to worry about typical web publishing headaches such as installing/administering server software, or making sure your data is accessible to the Server. With ArcGIS Online you upload your data after its been processed/analyzed, create your maps (including basemaps and content from other authors if needed), and publish the maps for specific people, groups, or the general public to see.