Although not strictly a zombie movie (in that its "zombies" are in fact who have been infected with a virus, and are not actually dead), is an excellent horror movie which uses many of the tropes and themes common to Zombie Apocalypse stories and subverts many as well. Its success helped to spur on the recent popularity of zombie fiction. If you're going to use fast zombies, then 28 Days Later is a must-see for ideas on how to do it right (as is the aforementioned remake of Dawn).
Ah Marie. You’re funny. I’d be cheering for you as the heroine of a zombie apocalypse story. Depending on exactly what you have, I feel like you might have something with those gardening tools.