I wouldn't recommend Border Collies -
i wouldnt recommend terriers either til the youngest kiddie is 5 at least. we got a terrier pup and he is just fab as a walking companion for me but at 9 weeks old he bit my 10 yr old daughter quite badly and aggresively when he wanted her pasta

and we have to be careful about feeding times as he has been known to start a fight and not stop. its alot better now he has been neutered but he still needs watching. terriers dont tolerate rough handling in the way a labrador does. if you are getting a labrador - please - be alert to the health testing, our 8 yr old lab is very lame to elbow dysplacia, but is the most loving dog ever. they are perfect for families but can knock little kids over by accident in their enthusiasm.
our gsd is a very lovely family pet, we spent alot of time training and socialising her when she was young, and she has always been a bit daft. people/strangers are quite daunted by her size though, she has never shown any signs of aggression but is a bit batty

we have a lhaso apso who is very lovely but incredibly jealous over affections. he has started a few fights over who was allowed to be stroked first, which left a permanent scar in my sons arm.
we had a lovely springer x collie as kids and she was a softy through and through

wev tried to rehome a rescue dog but werent allowed as we have children under 12. its a shame. but on a positive a puppy can be moulded into what ever you want. essential when your kids are so young and you have animals.
our little dogs are much cheaper to feed and bed than the bigger ones, and often come out with us for the day, when we dont have room in the car for the bigger dogs, but they also manage to wiggle under gates and wander off.