With all backcountry sites in Algonquin, you reserve for the lake, not the individual site; once you get there you can take any vacant site on the lake your permit is for.
Personally I wouldn't pick the Joes. They have motorboat traffic, cottages, summer camps and a lodge (which access by a private road), so although it's only one easy portage from Canoe Lake, I still find it a poor portage to "wilderness feel" ratio.
There are plenty of lakes you can backcountry camp on without portaging to get there. In the Highway 60 area this includes Canisbay, Sunday, Norway, Fork, Crotch, Farm, Whitefish, Rock, Opeongo, and Galeairy; but note that the last 4 of those have motorboats, Whitefish and Rock have cottages, Galeairy has a town at one end, and Opeongo has lots of big water that can get rough. The west end of the park is no farther from Toronto than the Hwy 60 corridor, and gives you portage-free access to Tim, Magnetawan and Rain Lakes. Neither is the south end and you can camp on Kingscote (has cottages). Of course if you're up for a short portage or two then the options open way up.
Study Jeff's Map. It makes the options pretty clear. Also shows which major game fishes are in each lake.
FWIW, the first time my parents took me and my brother on a canoe trip we were 7 and 3 years old, and we went to Pen Lake, one short portage from the access at Rock.