Staffies are indeed vocal. Mine never shuts up. In the case of mine, she barks like mad when the kids get in from school. And that's just excitement. (Sane when her dad gets in from work). As friendship says, it's impossible to know whether it's 'talking' or something more sinister without being there and seeing the tone of it/body language/context.
That said I'd be on the phone to the rescue tomorrow, asking if they have a behaviourist. Dogs Trust will give you access to a qualified, experienced behaviourist the rest of your dog's life but I know not all rescues have this facility.
I'd also start training with her, either one to one with a trainer/behaviourist (ask for recommendation at your local vet's or the rescue or both).
Whilst on the phone to the rescue, I'd ask if they know her full history. Is it possible she came from a place where children did something bad to her?
I once had a foster dog who, within a day or two, went for one of my teenage sons. It was only then the rescue (a breed specific one and one with a supposedly good rep) let drop that she had come from a house where she had been tormented by... teenage boys. So why let me bring her home to a house full of teenage boys? I was livid. She had to go back. They thought because I had loads of experience, it would be alright but of course, it was a stupid situation they shouldn't have allowed to happen. That was one reason when I decided to get my next dog, I went to the Dogs Trust as I knew they tend to do good due diligence.
Don't want to scare or worry you - just saying it happens.
Did the rescue ask you to bring the whole family to meet her, in kennels? If not I'd be asking them why not...
Hopefully she will settle down and if there are difficulties, you can work on them.
I know however excited you are about getting a rescue there is a bit of an adjustment period afterwards where, once the dog is home, you realise the enormity of what you've taken on and how much it will change your family's dynamic. But that is normal and will pass.