Any specific reason you don't want to test it all on your windows machine first? Get accustomed and then look into setting up a server?
Anyway, the workflow you posted is fine.
The detailed installation procedure varies a little from Ubuntu version to Ubuntu version. You'll find pointers for example in Install PostGIS on Ubuntu 12.04Install PostGIS on Ubuntu 12.04 or Unable to install the PostGIS extension to PostgreSQL on Ubuntu 12.04 LTSUnable to install the PostGIS extension to PostgreSQL on Ubuntu 12.04 LTS
You can load Shapefiles into PostGIS using QGIS DB Manager. It has an import tool. See for example Exporting shapefile to PostGIS database in QGISExporting shapefile to PostGIS database in QGIS
