Hi,
By now you may have your trip all planned, if not, here is my suggestion. Drive north of La Ronge to Missinipe or Stanley Mission.
From either you start your trip down Churchill to Reindeer River. Then up Reindeer River (mostly lake, practically no current) to Wapiskau River, then up Wapiskau to Brabant Lake. Same thing, not much current to go against, several short portages around beautiful falls.
From Brabant go south through Setti, Kemp and few other lakes back to Churchill (Mountain Lake) and to Stanley or Missinipe to close your loop. If you enjoy driving on gravel you can also park your vehicle at McLennan Lake campground and do this loop (slightly longer) from there. You'll see people on Churchill up to Keg Lake, then it should be pretty empty, maybe again boat or two on Reindeer, and then Brabant.
Not many goes between Brabant and Churchill and even less on Wapiskau. The route is technically easy, and doesn't have any super long portages (all below 1km), yet through beautiful country and never very far from civilization. For good route descriptions go to
http://www.canoesaskatchewan.rkc.ca/skroute.htm , routes # 32, 33, 34. Very good site if you don't know it yet.
Hope you'll have a great trip!