Thanks so much for all of the great replies and suggestions! It’s reassuring to know that I’m not the only crazy dog nut out there

. The first breed we tried was a pug and we quickly learned that pug puppies are ca-razy hyper. Which isn’t necessarily a problem if you have the time/patience and don’t have young children.
The second puppy was a Boston Terrier and while she was smarter than the pug, she was also very high energy and needed more firm/consistent discipline that we couldn’t consistently apply.
I really like flat-faced breeds. It’s just a preference thing. I’m thinking that when the kids are older, an English bulldog or an adult Boston Terrier would be a good match. Wouldn’t get a pug again because aside from crazy puppyhood, they shed like the dickens.
From what I’ve read while doing my dog research, bulldogs love children, are big enough that they don’t feel threatened when a small child bumps into them and are pretty docile and low energy—all pluses for my family life!
The only frustration that I’ve recently faced—and perhaps it’s a divine sign that now’s not the time—is that shelters and rescues are extremely picky and stringent about who they consider to be a potential adoption parent. I can understand being careful to not place a dog in a potentially futile or dangerous (to the dog or to a child) situation, but some of them really want to make you dance and jump through hoops such that I think that they basically believe that the only dog-worthy people are retirees, childless couples and single people

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Most dogs shed like the dickens. My Bulldog is a brindle and white that lives to shed on my couch and bed. He simply can’t stand me wearing nice clothes unless he’s decorated them with his fur! If you’re into non-shedders look into Poodles or Bichons when you’re ready. Otherwise, you’re going to have to deal with dog hair all over everything at least a couple times a year when they get their spring and winter coats in.
Short dog hairs have a way of clinging to fabric. If you decide to get a short furred dog grooming will be much easier and wiping it down after it gets into something or rolls in puddles is also much easier (we joke the Pits and Bulldog have Teflon fur), but getting their hair cleaned up is a challenge. A good pet hair vacuum is a must! Also, those little whisk brushes with the tiny matching dustpan commonly found at the dollar store is amazing for brushing off couches if you have the wrist flick down.
English Bulldogs are still bulldogs. They tend toward extreme stubbornness. Raising my Bulldog from a pup was a trying experience for the first 2 years and that was with the help and support of his breeder, my trainer, my family, and a great forum I found. I had to put a LOT of time and effort into training and clean up before he finally matured. I spent a good portion of the first 2 years of that dogs life with a spray bottle in one hand, a wad of paper towels in the other hand, a grocery bag for the debris on my arm and tears on my face. Bulldogs aren’t for everyone and if a Pug pup and a Boston were too much for you I can guarantee a Bulldog will be too much. As adults most are pretty calm and docile, Ike is now that he’s 7, but as youngsters or untrained they try the patience of saints!
I was raised with a Boston Terrier a lovely female we named Princess. As she was my first very own all for me dog I learned a lot from her. Bostons are Terriers. Anything terrier is likely to have a high energy level, a middlin to high prey drive, and they tend toward intelligence and stubbornness. Even the adults need a lot of physical and mental stimulation or they get grumpy and trash your stuff.
As a general rule, most dogs need firm and consistent training. You can’t just train the dog until it knows a few commands and stop. First, because they don’t generalize well and need daily reinforcement of their obedience in different rooms, indoor and outdoors, and in different settings. A dog that has a solid sit, stay, and come at home may not be so hot at it when visiting friends/family or when at a public place. Second, because a tired dog is a good dog and training is a great way to work their minds which tires them out almost as much as working their bodies.
Also, I have a few concerns about your research. Most breeders who have websites are trying to sell you a product. A lot of them aren’t going to tell you the downsides of their breed of dog because they want to make a sale. You want a reputable breeder who will list out all of the ways their breed of choice has made their lives miserable. If they aren’t telling you both the good and the bad, they’re lying.
I feel you on the rescue and shelter thing. My husband is a truck driver and was over the road at the time. I wanted a large dog to be my companion. I also wanted a dog that would alert bark in case of intruders. You know, like dogs have been doing for us humans since forever? Yeah…no. I explained I was alone at night with just my children a lot and that I wanted a large dog to pal around with me during the day, sleep with me at night, and bark if something was amiss. The shelter told me that expecting a dog to alert bark was wrong and I would not be a good dog owner…