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I second the idea that the pet store may not be the best place, especially for dogs. The reason is that in many cases the puppies come from "puppy mills." A puppy mill is a phrase that implies the owners don't treat their animals well and don't plan breedings that produce better animals - they breed for quantity, solely to produce a product to sell. That's no way to treat a friend.
While many disagree, my concern is that dogs from the pound are sometimes there for a reason. This could include anything from aggression to being not house-breakable. This may not be the best choice for a first-time dog owner!
There are also breed-specific rescue organizations. Google 'greyhound rescue" for examples.
Instead, I recommend you find a breeder who is a member of the American Kennel Club. These breeders meet a higher standard than your typical puppy mill. The goal of an AKC breeder is to produce show-winning animals. What they are selling are the ones that are perfectly good but aren't show-quality for some reason. You also get to talk to the breeder and you'll usually get a health guarantee.
There are so many animals in need of good homes, I like to think your best bet is an animal shelter as opposed to a store. Pets from shelters are very often well trained--they're just in need of someone to love them.