Hello joggeroo, I frequent both the doghouse and here and have both dogs and a ds with AS myself.
In our case, my ds has never shown any interest in the dogs (we had three until recently and have two now). I think to him they were always' just there' - although to be fair, they were here before him, so in some ways he's right about that, iyswim. He did show a tiny bit of interest in our lurcher when he was a pup, but only in terms of him being something new in the house and in response to all the attention the pup was getting at the time.
In terms of breeds, there are so many, but from my personal perspective you can't do better than lurchers and greyhounds if you are looking for patient, calm dogs that don't need to be walked for hours every day and are often particularly sensitive around children. They come in all sizes as well, from whippet size right up to deer/wolfhounds. That said, most of them aren't massively trainable in terms of physical assistance, if that's something you would require.
My own lurcher is an absolute sweetheart - he was a rescue that came to us from a foster home at 14 weeks old and is so calm, loving and sensitive, he would make a perfect PAT dog, if I had the time to do it with him. He is a big boy, but because he's so slightly built its never been a problem for us. Ds2 was just 2 when we got him and we now have a 2 year old dd and he's never once knocked over any of my dcs, as he always takes care to be extra gentle around them. He likes a couple of walks a day, when he runs like the wind for about 20 minute, before coming home flopping and proceeding to snore his head off for the next few hours. 
Many assistance dogs are actually crossbreeds though and are selected from rescues up and down the country. They are assessed for temperament and trainability and then go through a lot of training in order to make the grade. Clicker training is fantastic for this sort of training.
Have you considered contacting some rescue organisations asking their advice? A lot of rescues work very hard to match the right family to the right dog and the people that care for the dogs every day are best placed to know which dogs might be suitable for your family's individual needs.