There are a lot of breeds that fit MOST of what you want, and some individuals within breeds that may fit ALL of what you want. The LGDs fit the low prey drive, good with kids, etc, BUT they generally wont stay close to home without secure fencing and they may be bigger than you want.
Berners, Greater swissies and leonbergers are better at staying home, but again may be bigger and sloppier than you want.
Other breeds may fit the physical traits better but may be more likely to chase the animals.
When considering breeds, look at their original purpose and what that entails. Herding is prey drive, so many herding dogs are going to be very likely to chase animals. Same for gundogs - its controlled prey drive. However, since they were also selected for high trainability, they can often be taught not to chase. BUT, that requires EFFORT on your part.
Other examples - scent hounds - beagles etc, were bred to catch and scent and run. People followed them. So dont wonder why your basset hound won't come when called.
Also, dogs like herding and hunting dogs were bred to have endurance. This translates to needing excercise! Breeds like sighhounds and LGDs who only use energy in short bursts are generally calmer around the house.
I would sit down and make a list of each breed and the traits you are looking for and check the boxes that they meet. You may find you have to adjust your desires alittle.
