There are so many small breeds out there, have you looked at the ads on here, or checked out the shelters?It really depends what temperment you are looking for and what kind of time you have to spend on grooming etc, long haired, short haired - there are so many options. Google small dog breeds.
If you raise the new puppy with the cats and teach in not to chase early on, you should have no problems. Your dog will come to think of the cats as a part of it's pack. It's attitude towards the cats will reflect on how you behave around the cats. I have a big tom cat outside that just wandered up and made himself at home. He loves to play with the puppies. I keep expecting to start barking. The pups play and love on him. But my adult dogs were not around cats when they were pups so they tend to bark at him and want to chase him.
Everyone has a photographic memory.... Some just don't have any film.
Actually, there are some breeds that I just wouldn't trust around cats, even if raised with them as puppies. You need to really do your research and know what the breeds tendencies are. There are some breeds that love to chase small, fast-moving things!
I highly recommend the book, Paws to Consider, by Brian Kilcommons and Sarah Wilson. This book tells you both the good AND the bad on lots of breeds. It also specifies if a particular breed tends to be good with children, other animals, it's bite tendencies, how easy/hard it might be to train, etc.
I have 6 pit bulls and 1 rottweiler. All of them are great w/my cats. Now, the ferret is another story. One of the pits tries to flea her and she freaks out, but none have attacked the cage or barked or shown any agression towards the ferret, then again, their not left alone w/her. When raised with them as pups, your chances are much better. Just keep an eye on them and when playtime gets a little on the rough side, step up and stop them.
Some dogs just have a very high prey drive Janders. Huskyseehuskydo is a member on here who has mentioned several times that her sibes can not be trusted alone with her cats. I have a friend who owns an Irish Wolfhound. He can not ever leave the cats with the dog for the same reason. I'm sure some of it can be helped with training, but I would assume that certain traits just can't be overcome. IMO