Hi,
It's not usually a problem having cats and a puppy. Cats Rule OK! Especially if there are three of them. I had three cats when I got my first puppy. He got a scratched nose once or twice when he was pushy but he was a quick learner. A good way to introduce them is have the puppy crated so s/he feels safe and let the cats get the smell of the 'intruder'. Keep them apart otherwise. Once the pup knows cats are around and they are ignoring him -as they will after a couple of days - then let the first proper introduction be at feeding time. Cats nearest the door and high up if possible (worksurface) and pup on the floor by you. The pup generally finds the food more attractive than the cats. Just take it slowly and eventually you may have a heap of three cats snoozing on a sleeping dog as we often did. My Springers have all been fine with my cats.
As to the breed, my personal opinion is that I would not choose a terrier breed or hunting breed to live with cats - other people will disagree, of course. But remember that how a dog behaves with the cats s/he lives with can be very different to the reaction to a strange cat in the garden.
If a Springer is on your list of possibles then look at my website for info
Sgurr - English Springer Spaniels - Welcome and then look at Scherzando (in Devon) on my links and there you will find the finest examples of working breeds that make superb country companions.
Sgurr