Hiya, I have qualifications in canine behaviour, veterinary care and animal management. So hopefully I can help a little bit. Most puppies are nippy. I've got a lab cross collie and she nipped at me until around 6 months. Not aggressively but if she got over excited in play. You must remember also they are also teething. Staffies and jack russells can be more difficult to train but they are absolutely not aggressive dogs - I've never met an aggressive staffy that hadn't been train to be, I had met ones with no training though and they are usually just get so over excited but because of there muscle they can be difficult to control so yep training is essential. It is for any type of dog, but especially terriers. Give her plenty of things to chew on or she will find you shoes and anything else she can find - toys especially designed for teething are great for puppies. Also kongs are good. For training I suggest getting a couple of good books and a clicker (you can use treats to reward but puppy tummies are very sensitive so too many treats usually leaves you with accidents). Click every time she does something good - like toilet on the puppy pad. Positive reinforcement works so much more than negative. See if your vets has puppy interaction class, good socialisation in the beginning is essential so you can take her to play in the park when she is older with no worries. Any good vets will give you loads of support and advice. For terriers exercise is essential but be careful not to over exercise in the beginning when her bones are still growing, again your vet will be able to give you a limit for when she is old enough to go out.
I will say 6 weeks is a little too young for a dog to be separated from the mother, usually 8-9 weeks but it's ok, with love, training and support of your family I'm sure she will grow into a lovely dog. I'm not sure how old your children are but I would never leave any dog, no matter how gentle, with young children alone. This is just for your own piece of mind really. My dog is now 10 and she is as gentle as they come but I still abide by this for her sake more than anything.
She is absolutely beautiful. I hope you have many happy years with her. All the best