Some random thoughts:
How will your cats react to a dog? Do they have any experience with dogs in their house? It won’t be fair to them if they’re terrified, even if the dog is neutral or friendly towards them.
Definitely a fence.
A two-year-old medium-sized dog may live another 15 years. Your children will be 20 and 24 and probably long gone. It’s unlikely the 9 year old will walk the dog twice a day until he leaves home. Hopefully you parents will also take part in dog-walking and playing. (A fenced yard is great, but dogs are happier when they get to go places and for walkies with their humans.)
Some dogs are quite capable of chilling out for ten hours three days a week, but I’d for sure arrange with a dog walker or neighbor to let them out at least. I occasionally work long days and if I’m going to be gone longer for 8 hours, a neighbor comes over and lets the hounds out for a bit.
Your schedule doesn’t allow for a puppy (unless you can take it to work with you.)
Smart, working/herding/terrier type breeds are going to have more energy, need more exercise and stimulation and be more challenging, as a general rule.
After you’ve done your research and homework on general dog care and breeds, consider a rescue (either general or breed-specific) that has its available dogs in foster homes. The foster “parent” will be able to give you a knowledgeable assessment of the dog’s personality, traits, how it behaves with kids, cats, other animals and so on. I’ve fostered dogs for going on 20 years off and on and think that for newbie dog-owners, getting a dog with known traits is a safe route.
If you’re drawn towards a particular breed, take curlcoat’s advice and find a reputable breeder who may have adult dogs available - show dog that didn’t work out, or a dog that was returned to them, like that.
I’ve had dogs and cats living together for years. Dogs have included Rottweilers who have grown up with the cats, a JRT mix who also grew up with them (although I suspect she would kill a cat that wasn’t “hers”) and pit bull foster dogs. All my cats are dog-savvy, and obviously one of my criteria for a foster dog is “won’t kill my cats.” Last house: litter box was in the basement, with a cat-door cut into the door so the cats could go down but not the dogs. This house: litter box is in the mudroom, not accessible to the dogs. The cats are fed on top of the chest freezer, which is also in the mudroom.
A last thought on children walking dogs without adult supervision. Presumably you live in a place where it’s safe to walk a dog - no loose or stray dogs, etc. And that the child is fully capable of restraining and controlling the dog should something happen.