A good reference and a very good read is Pierre Berton's " The Invasion of Canada" and "Flames across the Border", a two volume set. They are likely translated into french given that he was a very popular Canadian author.
The books give particular insight into Leader attributes, the quality of individual units and city/town/fort capabilties/capacities - all very germane to the game scenario.
(Another book on the naval side is Barry Gough's "Through Fire and Ice". the story of the sloop (schooner?) NANCY. )
Quite good stories of Trafalgar vets fighting on Lake Erie, the variety of militia quality, the role of the Indians (and for many tribes/tribe groups, their independent foreign policy).
Finally, in the popular culture, perhaps only two people are remembered, both women, and both for the Candy and Baked treats companies: Dolly Madison (USA, president's wife, baked snacks) and Laura Secord ( wonderful chocolates, heroine of Lundy's Lane). Gen Winfield Scott ( a young officer) later went on to great things and a long career in the USA.
Other tidbits: Zebulon Pike, first to plant a Stars and Stripes west of the Mississippi ( in Iowa), who named Pike's Peak in Colorado ( as Captain Pike ) and died as a General in the battle of York ( now Toronto ).
HMS ST LAWRENCE, being built at Kingston, would have been one of the largest in the Royal Navy. If you go to Navy Bay, on a sunny day, the ribs of the scuttled vessels from the Rush-Bagot treaty are still visible in the murk ( well at least they were in the 70's).