No to a puppy with young children, especially those who are not tolerant of being nipped and mouthed.
No to a Parsons or other similar terrier too unless you're a very active lot and not wanting to do long walks... they can run and run and can become arsey and destructive if bored (as can any dog, only JRT et al need more exercise than your average poodle or Staffie IYSWIM).
Long haired dogs are great as long as you have a Dyson and aren't excessively OCD about dog hair
I'm going to c&p what I jus said to another poster on Doghouse, who wants a Labrador, because it's relevant here too (and I'm too lazy to write it out again):
My Labrador's not fond of young children and if I were ever to need to rehome him, heaven forbid, I wouldn't dream of letting you adopt him therefore. My younger German Shepherd, on the other hand, adores kids. You'd all love him, I'm sure.
What I'm saying is that there is no such thing as X breed being better than Y breed - it's down to the individual dog. If a Lab's the breed you want, great, go for it, but I'd recommend that you approach rescue with an open mind and you might be surprised and find a... oh, I don't know... Boxer, Jack Russell or crossbreed who is just perfect for you and your family. I see that happening quite a lot in rescue and have done the same myself - went looking for a young little collie cross girl but the dog which I adopted and which was perfect for us was a 9 year old ruddy great long haired white German Shepherd! Best decision I ever made!
Re a rescue dog... let me put it this way...
You've met, how many parents with horror stories about rescue dogs? 5? 12? 15?
I handle and interact with 4 times that many dogs in a single day when helping in rescue. So do my children. Our hands are still on the end of our wrists and we still have all 8 fingers and 2 thumbs apiece.
For every horror story you hear they forget the tens of dogs they know which are perfect. Scare stories are as gossip-worthy as they are newsworthy. People don't talk about the rescue dog which never got out, which never chewed slippers, which never snapped because that's boring.
I have loads and loads of them though and I could (probably do!) bore your ass off with them!
People also speak of "rescue dogs" when they mean the dog they got via the free ads when the owner didn't want him. But that's not a rescue dog! Or they speak of a "rescue dog" when they mean a pound dog, which is normally one which is a stray, is completely unassessed, where the new owner has had no homecheck and there is no back-up or support. That's not a rescue dog! They may mean the dog they took off Auntie Ada because she was too poorly to keep him but that's not a rescue dog either.
A dog from a reputable and responsible rescue will be assessed, neutered, vaccinated, microchipped, matched to the new owner and vice versa, bringing with him a lifetime's support and an agreement that the rescue will take the dog back should the owner not be able to keep him, even if that's in 10 years time. A responsible rescue will also home check which is as much for YOUR benefit as the dog's, so they can identify and iron out any potential problems before they start and assess whether the dog you have chosen is right for your family and environment. Contrary to popular belief a lot of rescue dogs are not unknowns from the pound without any history but come from family homes as a result of marital breakdown, unemployment, having a new baby and "not having time" or the owner losing their home. Even then a reputable rescue doesn't just take whatever the owner says about the dog at face value but assesses that dog before rehoming him.
Finally... gender.... I'm biased, I prefer boys (not least as after years of owning them I'd forget I had a girl and would still call, "Come along boys!"). Again it's all generally down to the dog's nature though and gender is purely a matter of preference.
HTH, if I can be of any use in identifying a suitable rescue or dog, please let me know. And sorry, should have explained, I'm an independent network rescuer as well as volunteer for a private rescue and owner of 3 large mutts. :)