Hi Evan, Welcome to our forum. I would look at local shelters and rescues. The shelters are over run, I have recently adopted two and they are wonderful pets. The nice thing is you get to take your family and find a dog who FITS your lifestyles. People have lost homes and some were just NOT NICE and either way many wonderful pets are available. One nice thing is they come most times w/shots and spayed and neutered! For a very small fee these dogs can be adopted. You face many of the same things you would in taking in any companion, maybe they need housebreaking or learning to walk on a leash and that is just part of dog companionship. Plus it is the fun and bonding that brings these pets close to you and your children! Good shelters will help you find a pet who is family friendly! Plus you have a chance to play or become acquainted before adoption. Personality of the dog is the key!
Please do not think about purchasing from pet stores these are puppy mill puppies and they have been ill bred and are just for profit which in fact is harmful and hurtful to animals in general since the parents live in terrible conditions and are just a means of money making. Look into puppy mills if you have a question or thought on that please.
Depending on the age of your children and their ability to be pet friendly..ie. not pulling ears or teasing and so on, a dog who is of any age will bond with people who treat it well. Some dogs may need more grooming and more exercise that is just one of the many things you need to think about before adopting. Some dogs such as ones who herd or are sight type hounds may be harder to train and need more exercise possibly a fenced yard or atleast secured as they see something and they want to herd it chase it and so forth. I have some and have fostered some and they are gentle generally just need a little extra attention. Many mixed breed dogs are healthy and lovable as are pure breeds. having had both I could not find it to recommend one over the other. You can also look on the net at pet finder.com at the many pets for adoption they are marked according to any health problems, cat, children problems and so forth.
We all have breeds we just love mine is Goldens and German S. but I currently have two hound mixes and a poodle mix. Two of the three are very child friendly and one is friendly with older children only. They are very intelligent and make wonderful companions. They love to have walks and play time, sleep in our room at night. But I have crates that I keep them in when I cannot watch them until I know what their needs are and habits may be such as chewing..that is generally w/ younger dogs but not always. And crates are great for house training!
Depending on work issues very young dogs may not be suited to being left for more than an hour or two at a time. Many older dogs can be left for various amounts of time depending on the dog. I would definitely think about that and purchase of a crate, for training. Crates are worth the investment! I never crate my dogs for more than 4 hours when I had puppies the need was different. During the nights they went out every hour or two until house broken.
I hopes this helps you think towards your future ownership, I wish you well in a search for your new companion!