I wear a lot of
Landsend.ca shirts. Their prices are in US dollars, but if ordered from the .ca site will include all shipping costs to Canada, taxes and duties (you can even collect air miles).
Their regular prices fit your budget, but especially in the Clearance section you can find good bargains.
Their 'Tailored Fit' is the slimmer fitting option and is as slim as my Brooks Brothers 'slims'. They won't be as narrow as the more fashion forward brands, but you won't get the blousyness of your typical ready to wear stuff.
~firebug (I rotate about 40 dress shirts with about 15 from Lands End)