If you have young DC, you will have better luck finding a rescue dog through the breed-specific rescues that foster the dogs in people's homes.
As for finding a breeder, you will get conflicting advice about what is good and what is bad. The first thing you need to do is decide what t you want to do with a dog (long or short walks, agility etc), and then think about breeds that fit that (along whatever aesthetic or practical considerations you have too - short fur, not too big, whatever).
Then consider health and what health tests are advised for the breed, and how important you think these are (for example, hip testing is still recommended in some breeds that have, on the whole, decent hip scores). I'd always want tests done on at least one parent for simple recessives that are common in a breed like PRA in spaniels. I would be less worried about testing for rare diseases.
Some people will say that you must go to the breed club to find a breeder but if you want puppies with at least one health-tested parent you can start to track down breeders and litters on ChampDogs. I have seen some really excellent puppies advertised there.
I would ask a breeder how many dogs they have (I'd cross off anyone with more than about 8 or 10, unless I was after e.g. a racing sled dog), how often they breed and why they breed. Some people will just be breeding their family pet because they had Great-Gran and have Gran and Mum and want another generation. If you want a pet, the puppies come from adequately health-tested stock (for example, the sire is known to be clear of any recessive nasties), the breeder has made sure that the sire and dam aren't too closely related, and the breeder will take good and competent care of bitch and pups, there is in my view nothing wrong with this arrangement. Or you can go to someone who breeds for the show ring or for work, and has a couple of litters a year - also good, provided they also tick the boxes regarding health, not inbreeding and giving the bitch and pups really good care.
Personally I do not care if a breeder is council licensed or not, but in my view you must ALWAYS see the puppies with their dam (if she had died I would want to see proof from a vet) and you must ALWAYS see them where they are being brought up: I would want to see a puppy with mum at least once before I collected it to take home. I would never buy a puppy from any sort of commercial facility (the sort where there is at leat one litter on the ground almost all the time, there are several dozen bitches, and bitches who have had 4 or 5 litters are sold off to 'loving 5* homes for their well-deserved retirements!') These outfits tend to produce a lot of popular crosses - decent breeders of said popular crosses do exist but are thin on the ground.