Well, I've done the introductions both ways (the cat first-then dog, dogs first-then cat) and I think the important thing is to make sure the cat has places she can hide in, and places to climb the dog can't get to. This way the cat has control of how close to go, and observe the dog from a safe place. Of course it depends also on how the dog behaves. When I got my first dog I already had my cat who had never even seen a dog before, I just brought the dog in, he was still such a young, small puppy, he never paid any attention to the cat, who observed the dog from further away. Each day she would come closer and closer, and make friends eventually. When I got my second cat, I already had two dogs used to living with a cat, but the kitten had never seen a dog before and was scared (the only time this cat has hissed and growled!). I first kept the dogs on leash, and after a little while, they didn't even try to get closer to the cat and I always made sure they never approached the cat, but let her approach the dogs. It took several days of this, or putting the kitten in a room without the dogs, and I even tried putting the kitten in a carrier on a table, while the dogs were loose, just to get her used to the dogs walking around. After a while the cat didn't hiss at the dogs walking around, only when they moved more quickly, and very soon they were all best friends.
The point of my story (I think) is that in dog-cat introductions, I personally think it's important to go on the cat's terms. Dogs are easier, you can restrain and train them (or especially with a puppy in a new home, they may not even pay any attention to the cat), and let the cats get used to the new situation on their own, making sure they are never forced into a situation they don't want to be in. Of course the same goes for the dog, the dog will most likely be stressed by a new home too, and you also have to keep in mind that they have to be able to get to know their new home and people too. I've never had problems with my dogs and the cats after the initial introductions, and my dogs are terriers, not exactly mellow... Not all cats will stand up to dogs if they feel threatened, my older cat would swat the dogs and growl if she felt intimidated, still does, but my younger cat will never do anything like that (even if in play the dog is on top of the cat and mouthing her throat, wrestling- the cat just lies there, obviously loving it
), so you have to observe and figure out what works best for your furry friends.