Why did filmmakers choose the particular dog breeds that are showcased?

A little history may have contributed to one decision. A Norwich Terrier won the 1994 Westminster Dog Show, and a documentary film maker, Leandra Little, followed it all the way.

I believe, however, that the dogs' owners drove the bulk of the casting decisions. The breeds were picked to complement the characters. For instance, Rhapsody in White, was owned by a very wealthy couple. A Standard Poodle seems like the kind of dog they'd own -- elegant, a princess. Likewise, Harlan Pepper, a country man, owns a stereotypical country dog, a bloodhound. What kind of dog would a well-to-do gay couple own? A fancy Shih Tzu, naturally. Weimaraners are a bit high strung and energetic, and much like the Swans capable of inappropriate behavior. From wikipedia:

Weimaraner requires appropriate training to learn how to be calm and control its behavior.

The Flecks, the most down-to-earth competitors, have the most down-to-earth dog in the bunch. If Winky wasn't in the show, it's not clear that anyone would pick out Winky as a show dog.

In short, they fit the director's vision of what kind of dogs the characters would own, and would help drive the story.

Because these dog breeds are easy to train.

Like on this page you can see which breeds are easy to train and why. click me

or this link