I'm a Brit in Chicago, travelling into the UK the same week!
The Oyster card only works in London, on the suburban trains, tube, (that's bart to you!), and buses. Outside of London you buy individual tickets, either a single (one way) or a return, (round trip).
https://tfl.gov.uk/TfL stands for Transport for London, and its the central organization that covers all transit, including river ferries and bicycle rental.
But book your trains outside of London ahead of time. Like 3 weeks ahead. If you buy after that, the price gradually creeps up, and buying on the day is just crazy money, don't do it.
Start here, to look at tickets, routes, and schedules.
https://www.nationalrail.co.uk/Airbnb is your best bet for central London, or if you don't mind a somewhat crazy hostel, then go to Abercorn Hostel in Hammersmith. Its a great location for transit, but without the downtown prices.
I actually lived in that building in the 1980s, but its much better now!
LMK if you need more help with travel or other planning. I won't be in London that week, but am aiming to get to the gigs in Liverpool and / or Birmingham. I have family at both locations, so I don't have a clue about accomodation there, sorry!