That's a personal choice. It is easier to get a puppy or kitten when you already have another adult animal because both can usually adjust to each other easier than if you were to try to introduce an adult member of each species. I have introduced kittens to adult dogs and puppies to adult cats successfully and had them become great friends.
It also depends on your particular cat. The best way to know if your cat would be accepting is to try the animals out together. It's more difficult with a cat since most cats do not like to travel in the car, but if you can bring the puppy to your cat, that would work. Just make sure all are safe and not overly frightened. If you raised your cat or know bout his or her background then you are in the position to know whether your cat would accept a puppy.
When I got my most recent cat I took each of my dogs to meet a number of different cats over a period of months to test their reactions and the cat I ended up with is awesome with them both! All three animals were adults when they met, but the cat must have lived with dogs before to blend in so easily with them and not be afraid.
Some dogs such as huskies are notorious cat-chasers but I don't think breed is much of an issue if raised with the cat from puppyhood.