The choice of school is purely personal preference. Do your research into each regarding costs, location, whats included and what isn't and make your choice from there.
BBVA provide the finance product, with BA as a guarantor, so provided you are suitable for a loan from them, then BA should back it. There are non-UK residents on the FPP, though I'm not sure of what their financial arrangements are.
It may be worth a call to recruitment once the window opens.