Prey Drive is something very important to consider, but obviously exceptions to every rule. Training is also very important.
If you're going for a puppy, I would say that you should avoid terriers firstly. I'm sure there are plenty of terriers that can and do live peacefully with cats (I've seen cats and Pit Bulls cuddled up just like that greyhound
), but in general, terriers are extremely high in prey drive because they were all bred to hunt something.
I'd be iffy about herding breeds because they too are bred for their high prey drive, although it's utilized in a different fashion from the hunting terriers.
If you do get a puppy, make sure you go through a good reputable breeder who does all the proper testing on their dogs to make sure they're physically and mentally healthy before they breed them. Well bred dogs (of any breed) are more likely to be stable than a brother and sister penned in the back yard for the purpose of producing puppies.
My dog is a mutt with chow-chow, german shepherd, and collie in her (and probably more)... None of which I would recommend for keeping with kitties, but my dog does great with the five cats. It doesn't mean she likes them, but they sure do love her. They rub on her, lick her feet, lick her ears (all of which they happily do while she growls at them), and she tolerates all of it. Very rarely, she'll even play with them for a short period of time. This is a dog who used to roam free and kill squirrels and rabbits. High prey drive indeed, but she knows what belongs to us and what doesn't (though she's still not allowed to chase wild animals).
If you're willing to consider gettng and adult dog, My personal suggestion is that you go on to http://www.petfinder.org
and select DOG, type in your zip code, and go through the results. Many of the rescues and shelters there work through a "foster" system where they have the animals in homes, so they're able to tell you if the animals are good with other cats or dogs, and kids, and any other issues they may have. You may even be able to arrange for the dog to visit your home! Adults dogs are good because you're already aware of their personality, so you don't have to worry about what they're going to be like "when they grow up." Also, there's no potty training involved