Years ago my husband, brother and law and father decided to do Drink Around the World. All I can say is, thank goodness for the monorail. I can't remember if they started in Canada or Mexico, although the Dis recommends starting in Mexico so you can really taste the good tequila.
Keep in mind that World Showcase generally opens at 11:00am and closes at 9:00pm. I'd start as early as possible so you can pace yourself and don't feel the need to chug in order to get into each country. You want to be able to actually enjoy those drinks! It's a small world, after all.