I'm in my 6th year of flying BA long haul. Wrt the question above, at the time I joined I was given the choice of short haul or long haul as I had more than 2000hrs. I'm not sure what the current state of play is on that one, but in any case the plans are always fluid. It has been known for new pilots be given a compulsory last minute change of type during their induction, although extremely rare.
Personally I think BA are a very good employer but I in no way share the view that it is the necessarily the gold standard that everyone should be aiming for. What works for you is a very personal thing.
For my part I do largely enjoy my time at BA, although some of the last 5 years have been tough (strikes, indifference from certain staff members, big company where you many not fly with the same person again for a few years etc) all being very different from what I knew. Regarding days off, I don't yet have the seniority to achieve trip lines and by a quirk of bidline this means I am just about the most unproductive pilot in BA. I've done 630ish hours in the past year albeit I work every single weekend outside of Leave/Duty Free Weeks. When I do progress to trip lines I will be working closer to the 800-850hr mark. There are no trump days/RDO/get out of jail cards etc for the most junior. My experience here has been pretty exceptional, it seems as most people progress quicker on their initial fleet than this, all about timing and luck, so good luck all you lot! If I was on the airbus, 2 weekends off a month would probably be just about achievable.
If you are joining now onto shorthaul I would think you would move up the list reasonably quickly so long as the recruitment plans are realised. If you are going onto the 744 progression may be slower but you will at least have the protection of seeded blind lines which can be useful in protecting a couple of days off each month. Unfortunately on the 777 we don't have this facility (not that that will be hugely relevant for anyone reading this as no DEP's are going 777 as I understand). And yes... now my 5 years is up I am eligible to change to a fleet where I will have the seniority to gain a degree of control over my roster.
In terms of numbers of days off, with no leave I'll typically get 13-15 days off a month in addition to 3 time assingnable days. These are basically days they could use you but they would have to let you know in advance (so not same day standby). I may work these blocks one time out of six say, roughly speaking.
I've not much to add to what has been said before but I would like to comment on a couple of points I disagreed with earlier. The pension is money purchase with the company paying in 12% of 95% of your basic, so 11.4% of basic to anyone outside of BA. Not market leading in the UK but by no means the worst.
I wouldn't say I feel particularly valued as an individual at BA in contradiction to an earlier post. It's a mammoth organisation and within that context they look after us very well but I'm well aware that I'm a small cog inside a giant machine. Go the extra mile, which we all do from time to time and you're unlikely to get any individual thanks.
To touch on an earlier comment, command time is anyone's guess. When I joined, in my interview they hinted at 12 years for shorthaul, 16-17years for longhaul (all with a pinch of salt of course). Now with the retirement age being pushed back to 65 all bets are off as over 90% have stayed on past 55 (the previous compulsory retirement age in BA). The consensus seems to be that we may start seeing retirements again as people approach 60 but beware any wild predictions. When the retirement age first changed the mean estimate was that the majority might stay on for 2-3 extra years and that has been fundamentally disproven. I'm in no way berating these guys/girls for staying on, but if a command is a key driver for you it's something to take into account. Minor expansion is planned which will hopefully mitigate some of the stagnation issues over the coming years.