I am not a proponent of choosing inexpensive rifles for use under difficult conditions, and big game hunting in Canada most often comes with weather and topography components which are hard on rifles.
As has already been mentioned Tradex is a great source for high quality used rifles, and a used quality rifle trumps the rifle designed as a poor man's hunting gun, yet the cost can be similar. It has been my experience that when Tradex describes the condition of their rifles you can take it to the bank. I haven't bought a lot of stuff from them, but the rifles I have bought have been excellent value (my Brno ZG-47 and my wife's and my nephew's Husky 1600s). Provided you don't get a rifle with a cracked tang, these rifles are shootable right out of the box, but they are also priced so that if you want some refinements, added right away or later on, that are best addressed by a gunsmith, there is room for that in even a modest budget.
Chambering wise, your best bet lies between the 6.5X55 and the .30/06. If you suffer under the caliber restrictions of Southern Ontario, the 6.5X55 might be your best choice. Regardless of which cartridge you choose, I would urge you to begin reloading as soon as possible. Moderate cartridges (all former military cartridges fall within the moderate performance level) don't need premium bullets to perform well on game, and being affordable to shoot equals more shooting equals becoming confident with your rifle more quickly. Cast bullet loads cost just pennies to shoot whose low noise and recoil combines with good accuracy makes them enjoyable to shoot. Full power ammo loaded with Remington bulk bullets provide good hunting fodder and surprisingly good accuracy.
