I don't have a chihuahua, but i take finding decent breeders and dog care in general very seriously
Are you just trying to pick the smallest breed because you don't have much room or something or do you love chihuahuas?
They're not very compatible with children because they are so small and frail and kids can be a bit clumsy.
For a decent chihuahua you are looking at upwards of £750. If you pay any less you'll probably more than make it up in vets fees.
A good breeder will be KC registered, have at a 5 generation pedigree, not rehome the puppy until 12 weeks (because it's a small breed), have breeding restrictions on the puppies, offer life time support, have the dam and sire tested for knee and heart issues and even have the puppies fully vaccinated too at that age.
If you was after a more rugged and robust breed, i'd go for something more like a smooth haired parson russel terrier - like a jack russel but without the stubby legs. Cheaper to buy too
As with all small breeds they can be snappy, so you must take your kids along to see both parents before you even consider a puppy. If the parents are all lovely and wriggly and friendly, the puppies very likely will be.
If the parents aren't comfortable with the kids then the pups won't be, even if raised around them, so walk away.