Some very practical issues for you to consider. Vets - is your brother willing to authorise you to be responsible for vet treatment in the case of an emergency? Is the dog insured? If so, he needs to provide you with the relevant details (policy number, contact details etc) as in some cases insurers have to be informed/consulted BEFORE treatment can proceed. This is really important, and if God forbid there was an emergency this is not an issue that should hold you up.
Vet contact details - depending on how close you live, will you be attending the same vet, or do you need to find and register with one near you?
Basic health care - find out from brother when dog was last wormed (and with what) and the dates/details of vax and flea treatments. Find out when they are due for renewal, and check with DB about his willingness to pay. Make sure you have poo bags in every pocket when you go out, in the car, and at home. Do a regular poo patrol in the garden. Also useful to keep in the car - wet wipes, spare bowl and water for hot days, spare lead,towel and spare treats. Think also about how dog is being transported - safety is paramount. You have various options including a little harness that clips into seat belts, or a crate in the boot. Depends very much on your vehicle/preferences.
ID - dog should legally wear a collar and tag stating name and contact details of owner. If dog is resident with you, it would make more sense for the details to be updated, so that if woof does get lost, she is not returned to the wrong address/a dead end. Microchip - if she isn't chipped, she should be. If she is chipped, then chip company need to be told of updated address and contact details. This is vital. As a staffie, she is vulnerable if she enters a pound. Legally, she has seven days before the Council can kill her or give her away. Be under no illusions, most Council dog pounds are overflowing with staffies - she would be the first in the queue for the needle. One Council near me kills one in three of the dogs that go past their seven days without being claimed.
Dog training - most areas have dog training classes where you can learn basic obedience and improve leash walking, basic commands like Sit, stay and recall. You will both benefit hugely from the lessons - it helps bonding enormously and you will find a nicely behaved dog is just so much easier and more fun to live with.
Food - find out from your brother what she is fed and stick with that for the time being, at least until she is settled in. Presumably she will come with a food bowl, water bowl, dog bed and grooming stuff?
Other family members - be very clear with other family members about how they should behave. Key points include things like respecting her boundaries by not poking, prodding, grabbing or pulling her, not feeding her scraps, not leaving food down where she could eat it (especially if potentially poisonous like raisins or chocolate)and being very careful about open doors and gates. I would also look carefully at your garden fences and if possible make sure they are strong and safe for her.
Good luck!