Having two, of course I would recommend getting a staffy! www.thekennelclub.org.uk/item/87 They are great with kids and so much fun. :) Rescue centres are overpopulated with them (mostly because of idiots who buy them thinking they will be fighting dogs and they turn out to be old softies - but that's another story) and they are a really rewarding breed to take the time to train and live with.
(Although should probably add a disclaimer that they're very high energy dogs and not for anyone looking for a quiet life.
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TheButterflyEffect Staffs are actually not one of the breeds you'd typically say have big health problems - no more so than, say, labs - another popular family dog. They can suffer with eye problems. Did you by any chance see that BBC3 programme on all that clandestine pedigree stuff a few years ago? Staffs don't tend to have big problems caused by 'inbreeding' like the King Charles Spaniels/Boxers/GSDs (all lovely breeds btw!) I remember from this prog do, because they are so widely bred (in fact, there are too many people breeding too many of them but again that's another story). But as you say, all breeds have their problems. OP, if you are going for a puppy, you could check with the breeders that the sire and dam (if not pups themselves) have had testing for hip/elbow dysplasia and eye problems. They can get certification for this. It will potentially save you on insurance and vets' bills in the future!
Funnily enough, like TheButterflyEffect, I'm not much keen on Springers, have met some nice ones but more unpredictable ones. Not a breed I would choose to have around my kids but then again I've never owned one and many people say the same thing about staffs, so if I'm wrong I'm happy to be corrected, my opinion is just based on experience.
Otherwise, I have heard that pugs are great with kids, if you're looking for a smaller breed, but again never owned one so can't comment too specifically!
If you are looking to rescue, you have your pick of lots of lovely cross-breeds at your local centre.