We have a Soft Coated Wheaten Terrier, she is lovely. 
She is 13 years old now and has accepted the transition from being my constant companion and training partner to having one, then two, then three children and two other dogs to contend with, with amazing patience and grace.
In our case, she has almost never barked in her entire life. In fact I had to teach her to bark on command as she didn't even bark at the front door when I was in my own with her. She has also never dug anywhere other than on the beach (and I had to teach her to do that as well!)
She is a real little brainbox as well, having done heelwork to music, agility and obedience and gaining her gold good citizen award when she was just 13 months old. So they are highly trainable and in fact need to be trained and occupied.
Obviously, we took her to lots of dog clubs and socialisation classes and she is probably the most sociable and friendly dog we have every owned with both people and other dogs.
They are terriers and while they tend not to be as 'terriery' as say, a Jack Russell, they do still retain a fair amount of the terrier feistiness. That said, they're not snappy or yappy in any way.
Like all dogs the pup will need to be taught to respect people (especially children and babies) just as the children should be taught to respect dogs. Regardless of the breed of dog, or how reliable you may think they are, you should never leave a dog and baby/child alone together and we have a dog gate between the room the dogs spend the majority of their time in and the rest of the house for that very reason.
As minimu said, they are very lively dogs and tend to love-love-love people, which can lead to them jumping up if they aren't taught not to from a very young age. In fact the only negative thing I can say about my girl is that she is a little too friendly and as a youngster would rush up to greet anyone and everyone she saw whilst apparently going deaf to any of my commands. I ended up having to spend a lot of time training her around this.
Sorry, I'm rambling on aren't I. I guess I noticed this thread and jumped in because my girl is very poorly at the moment and we probably won't have her for much longer. 
I thought we were going to lose her at lunch time today, but she has rallied a little and is happily sleeping in her basket at the moment.
After 13 happy years with my old girl, I would happily recommend Wheatens as family pets, with the usual caveat about teaching both dogs and children about respect for each other and never leaving them alone together - even for a second. But then I would have the same caveat for any dog.
HTH