he is 19 inches at the shoulder: Hercules is at the pool with his slightly smaller brother Blaze (46 lbs) hope the link works, never tried it before
I will 3rd (or 4th) a nomination of the Boston Terrier. a low maintenance dog.
Someone mentioned basenji*s upthread. We loved ours and it meets most of the OPs criteria, with a couple of exceptions:
- They always seem to be rated as one of the least trainable breeds, although they are very smart, they don’t take instructions well (see cats).
- The don’t bark, but they do “yodel”, although ours didn’t yodel very often.
We currently have a chihuahua/something (some kind of terrier)? mix, and I thought it couldn’t bark, until fairly recently. But it doesn’t bark or yap or do much at all. She is a rescue animal who lost a leg to a car, so she takes some special consideration, but absolutely loves her mama and the kids. Me she’s not too wild about, but she’s become tolerant.
*This pic is what ours looked like.
Beagles will bark. Since they can not take a bugler down, they will alert you if someone is around. You will also know if a rabbit, a raccoon or a cat is in the area. Those are good things to know. I am pretty sure beagles look down on people as being bipedal no-noses. Very inferior .
As far as dogs are considered, it is a well known fact that there are golden retrievers - and all the rest. 
My BIL / SIL have a Wheaten and she’s a great dog - not hyper, just an all-around nice dog. Not so small as to be intolerable to a boy, not so large as to be tough to handle.
At such point as we think we’re ready to get a dog, Wheatens are definitely in the top 3 breeds we’ll look for.
Someone I know has a labradoodle (mix of labrador / poodle) and she is also a very nice dog. I went over to their house for something once and the dog didn’t know me from adam, but just stood there calmly, watching me, wondering if perhaps I’d care to offer up some pettin’s. I was sorely tempted to indulge in a little dognapping 
Why do people say things like this? OF COURSE you can get purebred whippets at rescues; like all other breeds, irresponsible people have produced more than they can be bothered to properly deal with.
Ten seconds of Googling produced this:
Whippets are sensitive but not that bad. I have no problem telling mine ‘no’ in a forceful tone. I haven’t found any other ‘negative’ reinforcement necessary except an occasional light swat on the rump to get his attention. If anything, the sensitivity makes him more responsive, unlike a more stubborn breed.
If you do go with whippet, the cat issue may be a concern if the whippet has not been around cats before. You also need to commit to letting a whippet run daily or near daily.
I’ll third this.
I was a cat person for years, and I’ve had a Shiba. They’re wonderful dogs, but they have all the bad qualities of cats, not the good ones. Plus, they have a lot of doggy needs as well.
Unless you’re prepared to spend a lot of time out walking & running this dog, or if you have an absolutely huge fenced yard with another dog for it to play with, don’t get a Shiba. They so need space to run, and a ton of exercise. And they’re incredibly independent. Ours was constantly trying to get out, even though he did have a really big yard to play in AND another dog to play with.
I have pugs now, and I have to say - if you like cats - a pug has all the BEST qualities of cats & dogs. They cuddle and sit your lap like cats, they don’t have a huge need for walks, but at the same time, they come when you call them, and they looooooove you in that way that only doggies can looooove someone. I’ll never have a different breed of dog; I’m a pug person now.