What is the easiest way to get OSM data into a shapefile projected data format for QGIS? Sounds simple but I've run into problems with this before.
Try WeoGeo - it is a while since I gave their free OpenStreetMap download service a successful test but I believe it will meet your requirements.
There are several script called
osm2shp that do what you want, or you can use QGIS.
For an overview, see this wiki page
Once you have the data in a shapefile, you can reproject it into any CRS you want.