PA, your career path assumption is pretty accurate. The only major factor that's different from when I was a low-hour, newly qualified fATPL holder is the willingness of mainly low-cost airlines to offer "Pay to Fly" packages. I deplore these, they are taking huge advantage of guys/girls who just want to fly. That said, if you are desperate to get your 500 hours in an Airbus or similar then I guess its a means to an end.
To put things in context, when I qualified in 1996 British Midland used to see 737 type ratings for £9k. If you completed the rating BM would give you an interview.....It didn't mean they had any vacancies, they just gave you an interview.
BA is a good company, they treat us fairly well and is certainly considered a career airline. Like all things in life, compromises may have to be made in order achieve your ambition.