As a junior DEP, I would choose 747-400, 777 and 7576 in that order.
The reason being, at the bottom of the pile, there isn't a great deal in it between the -400 and the 777. Ok, on the -400 you will probably get a seeded blind line, which means you will get something like an LAX and four 'guaranteed' days off around it but otherwise you will get largely two-crew trips (think JFK, PHL, LOS, etc.) which is what you would get on the 777. There is a seeded blind line trial on the 777 at the moment which, if it goes permanent, will mean a seeded trip (probably an East Coast, as most of the trips are of that sort of nature) but with the same 'guaranteed' four days off around it.
The 7576 does a mix of LH and SH flying, although the longhaul trips (generally to Africa although there's a MAN/JFK and NAS) can get quite senior so you'd be doing mostly shorthaul. It is considered a good fleet though.
If money is an issue, you will be paid more or less the same on the -400 and the 777, and marginally less on the 7576 as BA consider it "Medium Haul".