When I got my kitten Baz, Cody my staffy was 3 years old and Daisy my Cairn terrier was 6. Both were absolutely fine with him. My staffy would play with him and mouth him but never try to hurt him. The only issue we had was that Baz would often try to suckle from Daisy and she would let him. Daisy started getting really sore teats so we had to put a stop to that!
Baz is now 5 and he and Cody have a very close bond. They will share a bed together and Baz will always greet Cody with a face rub and brushes up against him. Cody sometimes isn't in the mood and will chase Baz away or mouth at him and Baz knows what this means and will give him some space. Daisy is also fine with him but they are not as close however they will share a bed together. Sometimes Baz will groom Daisy's ears which is cute!
We got our second cat, Zelda, 4 years ago and she was a 2 year old who was given away for free as an unwanted pet. She has not bonded with either dog. She is not scared of them and there is no aggression between any of them but she just avoids them and acts like they aren't there. The dogs also just ignore her.
I think it was better getting a kitten not an older cat as the kitten grows up used to the dogs.