Dog breed choice? we love the coonhound and saluki

We are finding it very hard to find the right dog breed choice for our family. We are a family of four. Two daughters age 7 and 8 and a siamese cross cat age 15 yrs.

we are looking for a puppy or young dog that we can take for walks and runs off a lead. We live next to a big village green but near a busy road.

We tried a rescue coonhound. We loved him very much. He was a lovely character. We just found him to strong on walks for our girls and a little too big for our small cottage and read he would run off if not on a lead. We were also worried for our cat. We didn't ever leave them alone together as worried what might happen to the cat. Maybe we should have persisted past the two week trial as we miss the dog very much. We love elegant looking dogs like the Saluki too. We liked the markings of the tan coonhound. Any advice be so much appreciated.

Are you interested to some big size breed? I mean boxer?

I guess I might ask here since the title of this thread relate to dog breed choice. Does anybody know a good breed to live with small apartment? I knew some small dog breed like Shih Tzu but it might be costly to get that kind of breed.