I would like to plot a trip/track (stored in the postGIS database as long. and lat.) on the OSM map, offline, based on the OSM shape files which are locally stored. Could anyone give me directions how to do so?
QGIS is a nice platform for various formats, as it uses GDAL and other tools to make data usable. OSM can be accessed in QGIS directly as a raster, via a supplied plugin, and you can use all sorts of vectors on top of it.
I like QGIS because it manages various exotic projections seamlessly, and I need it for that particular reason. It also supports other open maps, and WMS online sources.
If you are new to QGIS, go for a 32 bit version, and install Python first.