The Canoe Lake-Big Trout-Canoe Lake loop I will describe is one that I've completed over a dozen times. It is a classic route in the park and it is my number one choice for guiding my outdoor education classes. It can take a leisurely 5 days, or as short as 2.5 days. With my large groups I do the route in 3.5 days, and 3 nights as described below. The route has a great mix of small creeks, big lakes, and progressively hard portages.
The route starts at the Canoe Lake access point along highway 60. Highway 60 is the main highway that runs through the middle of the park. Cell service is accessible along the highway but a short 1 hour paddle off the highway and the cell service dies. Be prepared for backcountry camping beyond this point and make sure you have the adequate skills (canoeing, portaging, water purification, navigation, bear safety, wilderness first aid, etc) and knowledge before entering the wilderness area. Be sure to pick up your permits from the park office, rent any equipment items from the Portage store, and use the flush toilet for the last time. Campsites in the backcountry have a limit of 9 people and have only a fire pit and a small pit toilet as facilities.
Day 1-Canoe Lake to Burnt Island Lake (half day): Heading north along Canoe Lake, enjoy the old cottages and summer camps on the shores and islands. Stop at the Tom Thompson memorial on your way into the narrows at the north end of the lake. Veer right to the Joe Lake portage trail and portage the flat 250m trail around the dam. There is an outhouse along this trail if you need it. Paddle under the bridge hugging the right hand shore of Joe Lake moving through a narrow and into Little Joe Lake. On your right, you will see the Arowhon Pines Lodge, the setting for the movie Indian Summer, and the last man-made building you will see for days. The next short 165m portage you encounter is easily skipped in high water. Paddle through the creek to start the longest portage of the day 435m. A short paddle across Baby Joe lake and through a short final portage of the day 200m (make sure you go right at the fork!), and you'll be on Burnt Island lake. Depending on the weather and time of year, there are many sheltered campsites and wide open campsites along this lake. Listen to the loons as dusk hits.