There are dog breed characteristics/dispositions... and then there are also the dog's own personality and if they like children or not, etc.
Each dog, will be different. Though tendencies will occur, each individual dog is not homogeneous, per breeds.
Then there are the health specifics, of a breed.
As Julie K. mentioned.
I have seen Shitzu's (of friends)... that were very snappy.
And barked a lot.
This is the spectrum with any dog.
As is with their upkeep or need for grooming or not, etc.
A rescue shelter person, should know the personalities of their dogs... and IF, the specific dog, regardless of breed, is good with children.
Children... often fall in love with any dog... they are after all, very cute.
But you need to research breeds, and their dispositions etc.
For example: "King Charles" dogs (I have friends who have this dog), are considered to be "lap dogs" and, were bred for this reason, way back, for the Royalty. And they are often good with children and a more 'calm' dog.
Some dogs, like say a German Shepard, are very different and were bred for different reasons. Thus, their tendencies are more for protection and they are very loyal dogs. I had one. But I would not say, our dog was a 'lap dog.' Though he was very loving.