Take your new puppy to the vet for a “pre-purchase exam” as soon as possible. Even though you've already paid the landlord, this is called a “pre-purchase” because most reputable breeders and adoption organizations allow a probationary period (often 72 hours) before the deal is finalized. It's a good idea to schedule an appointment with the vet the same day you pick up your puppy to quickly identify any existing problems. Your first look should be at the litter in a group.
If there are four puppies and three of them keep arm's length or suspiciously deceive you, this is probably a very risky litter. Most families make a mistake when they choose bold, vigorous and energetic puppies that jump on you, grab all the toys, start all the fighting bouts, grab the leg of your pants, and pull fiercely with adorable puppy grunts. Too many puppies end up being abandoned or destroyed dogs because people don't see beyond that pile of cheekiness and consider the rational and practical aspects of owning a dog. Although puppies are not fully ready to leave their litter until they are between 8 and 12 weeks old, a puppy's personality begins to emerge at 5-6 weeks.
Sometimes the rest of the puppies won't want to play with that particular puppy because he has already shown signs of being a bully. While the vast majority of puppies grow up to be well-behaved, healthy and adorable dogs, your chances of getting the right puppy for you will be much greater if you have a simple checklist beforehand to help you make your decision. Beyond being technical about any particular disease, you need to have a general feeling that the litter, as well as the particular puppy you're considering, are showing all the signs of strong, healthy puppies. These breeders want to meet their puppies and then match them with the right families (and send well-adapted dogs to advanced training programs).
If the mother is relaxed, your puppy is likely to be too, since puppies mostly inherit their mother's temperament. Remember that it's completely normal for new puppies to whine the first few nights away from their litter and mother. Don't be frightened by a litter that looks “collected”, with only one or two puppies 12 or 14 weeks old. The biggest or fattest puppy in the litter may turn out to be the greediest; he probably pushed the other puppies to get the most food.
The leading cause of death for puppies under 12 months of age in Australia is euthanasia due to behavioral problems. If you choose a litter from an experienced breeder who has raised a healthy, well-formed dog to a social and well-trained stallion, then it is likely that all puppies in the litter will turn into happy, healthy and trainable dogs. So you've decided that those puppies in the toilet paper ads on TV look like a lot of fun and you have to have one.