For the purpose of your project I would recommend to use QGIS for creation of layers (shape file and rasters). QGIS can use a lot of the mentioned functionalities of GRASS as it has a GRASS-plugin.
For serving the shapes and rasters online in a webmap I would use geoserver to serve them as a wms (web mapping service) and consume it on the same machine with openlayers.
we have a lot of content regarding this:
you may find a good overlook here: http://www.digital-geography.com/types-of-web-maps-concepts-and-possibilities/
best wishes, riccardo