to Clarice about your views on rescues. Reputable resuce charities will provide a homecheck for you first, to ensure you are the right home for the dog, then will carefully match you with a rescue dog whose temperament has been carefully assessed. The dog will be neutered, microchipped, vaccinated, flea treated and up to date with medical/worming/dental treatments.
An adult rescue dog who may well have come from a family home through no fault of its own (divorce, family breakdown or redundancy being frequent reasons that are unrelated to the individual dog's temperament) will make a wonderful pet, while a cheap, unsocialised pup from a puppy farm could be years of behavioural and medical headaches.
Further, rescues provide ongoing advice and support for new owners during the life of the dog, and all reputable rescues will be happy to take a dog back if at any time in the future (say ten years) the new owner is unable to care for it.
Not all rescues are cross breeds - most breeds have their own rescue organisations/websites and many work nationally. You will also find all breed rescues in your neighbourhood - there is undoubtedly a wonderful family pet out there for you if you are willing to do a bit of homework.
Some rescues will not home dogs to families where children are under 5, so you will need to check this out. Rescues do not do this because we are child hating weirdoes but because sadly having small children is the NO. 1 reason for rehoming dogs (usually lack of time) and it is important to remind you that a dog is NOT a toy. Your children must not be allowed to be alone with it, and must be taught from day one that it is not acceptable to poke, prod, tease, sit on, or otherwise hassle the dog. If you genuinely cannot sign up to this level of supervision and this would not sit well with your style of parenting, then you should probably wait until your DC are older.
You haven't mentioned it, but it is also worth making sure that all the adults are signed up to dog walking, poo patrols in the garden and you have done your budget forecasting to include food, vets bills, worming, vax, grooming, and insurance.