Having comleted the Cadet Scheme about a year ago, some of this may be out of date....
BA pay for all accomodation, and give you £30 per week pocket money. I was in America and ended up spending about £3000 on top of that. GASP! I hear you cry! The life style is up to you really...BA do pay for your journy out there and one trip home during the year, but if you want to go home more than that, you'll have to pay for it yourself. Also we all bought cars out there...but if you want to keep costs down, transport is provided...but you'll find it a bit dull if you don't spend some money out there.
As for preferences when you join the company....you say what you would like, they then are told what places are available, and everything is dished out in age order on the course, (oldest has first choice). On my course, over half went to LHR (737, 75/76, and Airbus), and only a few went to LGW. Although I think that most at the moment are going to LGW. The Regional placements are not as common.
Pay...you do get some expences during training, but only if you're NOT at LHR. They provided hotels and all the usual night stop allowances. And during line training, the only thing that you don't receive is the Flying Hour Rate for the first 15 or so sectors that you have the safety pilot with you. I'm now bring home not less than £1800 per month (most of the time), but you do have to pay for you food down route...
Hope this answers some of you questions ,
HG