It really depends on how confident you both are with dogs and your experience with them.I would say pretty much any breed would be fine, and even more tempted to say that if you contact a few of the breed rescues with your requirements they should be able to put you in touch with a dog sturdy enough to put up with children and a track record of letting children pull them about. A mature dog who has seen it all, been through it all, and come out of it with a wagging tail is one that I would generally recommend for first time dog families.
A pup can be good, but you have to be aware that they could go through a nippy stage (not all do, but some can) which requires patience to get them out of. Having been on the end of many a distraught call over new parents/dog owners who don't know what to do because their hormonal juvenile has nipped their young bairn i'm always wary of advising pups to go into homes with young children. Also be aware that if you go the rescue route many will not rehome to people with children under 5, some have even higher age limits of 12-14 (some will though, it all depends on the rescues near you).
If you introduce a dog to the house don't get too paranoid about it otherwise you risk fulfilling your worst fears. I personally do not think any child under 10 should be left alone with a dog, there should always be adult supervision. As I said before you should take the time to teach the children how to interact with the dog appropriately, ear pulling and stuffing fingers up noses will happen but it helps minimise the risk of them getting into an accident if you can help them understand they have to be gentle and respect the dogs privacy. The Kennel Club have an excellent pack for people wanting to help their children understand dogs, and for parents who want to introduce a dog into the home (I think ... it's been a while since I did anything with that).
I would be wary of breed stereotypes. Whilst they can lean towards being of a certain disposition you have to know where they come from and make sure you give the dog a chance to live up to this. As a groomer i've seen sappy Chow Chows and aggressive Springer Spaniels, it all depends on nature AND nurture. Appropriate training of both dog and child can help, and older children often enjoy getting involved with dog training. Another thing I would say is make sure the dog knows how to take treats "gently", it's something I insist on teaching my muttlings before they go anywhere near children. Same goes with teaching them not to jump up, not to beg at the table, not to pull on the lead, all of that fun stuff.
If you are determined to have a pure bred pup i'd recommend going to the Kennel Club site and reading the breed standards, find a dog you both like and then start looking at the breed clubs/researching breeders. But again, because i'm biased, I would say don't dismiss older dogs. Rescues such as the Oldies Club have websites which list dogs according to whether they're good with children/size/activity level and a whole host of preferences. Even dogs aged 7+ can be active enough for family life, yet calm enough not to knock the children about all the time. I'm not just saying that as a campaigner for older dogs, but this is genuinely my normal advice for anyone considering a family dog, especially if one of the parents is slightly more nervous about the prospect than the other.
Be aware some do recommend that before getting the first dog children should be aged 6+ so that they should, hopefully, have learned enough of self control and respond to direction.
