Algonquin was where I learned canoe tripping.  It is an amazing park with a long history.  It is ridiculously beautiful.  That being said it is also, as ST points out, close to Toronto and is along with Killarney, the busiest canoeing park in Ontario.  If WCPP has under a thousand paddlers each season and Wabakimi under 2000, Algonquin has over 10,000.  Busy.  So if you're looking for solitude of the sort you might expect at WCPP - days or even weeks without seeing another human - forget it.  On the other hand there is no motor boat traffic in Algonquin.  There are no fishing lodges.  It is a dedicated canoeing park.
The northern part of the park, the Kiosk entrance, by virtue of the fact that it is furthest from Toronto, is somewhat quieter but really not by that much.  Shoulder seasons will be better than the height of summer but in any case you will be wise to book your trip many months in advance to assure that you will have access to campsites.  You don't have to say which specific campsite you will be staying at but I believe you do have say which lake you will camping on each night.
A couple of leisurely trips: Put-in at the Rock Lake campground (#9 on the map) and paddle south.  There are two ports, the first is 375 M, which takes you into Pen Lake.  At the south end of Pen there is a second port, 275 M, which takes you into Clydegale.  You could reasonably do Rock to Clydegale in a day and it is a nice lake to hang out and base camp.
Another nice little trip is to put it at Shall Lake (#17 on the map) and paddle over to Booth Lake.  There are 2 ports.  The first, you can paddle up in the spring and is, at any rate, a mere 90 M.  The second is 550 M.  Both are very easy.  Booth is a good lake for fishing - Northern, Smallmouth and Lake Trout.  I've caught some nice 5 and 6 pound smallies in the Fall.  Booth has lots of excellent campsites and is a good place to base camp.