Jen, if you are hell bent on getting a pup rather than a rescue, you need to start by you and your husband thinking about what breed of dog you really want. Research your breed carefully, and give a lot of thought to your lifestyle, finances etc and be honest in your assessment. A lot of people get a high energy dog (such as a dally or a pointer) thinking that the dog "will get them out of the house" - this simply isn't realistic if your only current exercise is to waddle to the car to drive to McDonalds.
A year later, the dog is climbing the walls with boredom and ends up being rehomed with "behavioural issues". Not saying this is you, but hope you can see what I mean about being realistic.
Take a look at the puppy threads on here - you will get a realistic assessment of what it's like to live with a puppy and small children (not easy, but doable). Also be realistic about the practicalities of dog walking with three small DC.
Once you understand what breed you want make sure you really, really understand the breed, and particularly the health issues. The KC website has a lot of info on the dozen or so breeds which are high risk (Cavs, St Bernards and a few others - these have massive health issues and personally I wouldn't go near one with a bargepole, sadly) .
Have a think about what you will do with your dog, once it grows up. Is it going to be a gundog? Field trials? Showing? Obedience classes? Agility? Flyball? Cani X? Loads of activities these days all requiring different things.
Good breeders will NEVER need to advertise on dodgy websites. They have litters infrequently, and are because they care about the breed and put a lot of thought into improving it. Often they will be heavily involved in showing, working etc. If they aren't that's a red flag. They will know their dog's pedigree inside out, will understand all the health issues/testing, and will grill you like the Spanish Inquisition about your suitability. They will not mate dogs because of "an accident", because the sire lived nearby, or because they thought it would be nice for the kids to see puppies.
Alternatively, you could go to a reputable rescue. Many will have pedigree dogs, will have foster tested them in homes so are suitable for children, and will offer lifetime support and backup. Many rescues often have puppies as well.