A good 30-30 or a 44 magnum in a lever action rifle would be a great choice. Stay with one of these two for one simple reason. Ammo is CHEAPER. Nothing wrong with the other cartridge recommendations if you reload, but if not then you will shoot the 30-30 or 44 magnum for less money, it is that simple.

If you want a scope then buy a Marlin. IF you want open sights then go with a Winchester. $600 is a bit high, you could buy an open sighted rifle and a lot of ammo for that price. Tom.