Don't put the SO job down so single-handedly
WWW. Plenty of us actually did it for a while, and learned a hell of a lot; and not just about getting Volmet etc. mostly about the people-handling and airline operation skills. It's all down to your personal attitude, and how you approach the job... not necessarily the best way to start an aviation career, but it is a foot in the door at certain carriers. Nor is it something to do for a long time either, and should be consolidated with other flying, a structured sim. program and followed up on a small and violent type like a 737/T-Prop, but neither is it the trivial waste of time you characterise it as.
We did find ourselves with about 400 hours crossing the ITCZ, negotiating levels (creatively!) with Calcutta and Delhi, sitting over Siberia in winter with Europe Cat III on absolute minimum fuel. All the time learning from the experience, and most importantly seeing how the very experienced and culturally diverse crews we were flying with dealt with the operation.
Cart before the horse, certainly, but now in the LHS I find myself often referring back to the experience gained in CX. That, by definition, cannot have been a waste.
Anyway, enough already, to the question at hand; my mob would put cadets onto the 757 in the past, with the 767 coming up after about 6 months on average. However, to fly the 777 on ETOPS (and possibly the 767 ETOPS, but not when I flew it in 1996) required APIC qualification (Acting Pilot in Command) which basically meant you had to be suitable for command, with an unfrozen-ATPL and a few other hurdles succesfully crossed. For those reasons you are unlikely ever to see low-hour P2's in the RHS on the fleets that can require in-flight relief, ie, the long-range 777's, 330's, 340's and 744's of this world.
The largest you can "realistically" expect is a 737... the best place to start an airline career is without doubt one that builds exposure and handling experience. Time spent in a turboprop or something smaller than the jets you mention at the top is
never wasted.
Some of this may be innacurate regarding other carriers policy, for that I apologise, but regarding BA that seems to be the current position of the goalposts. As you are well aware, they are constantly in motion, damn things!
Good luck.
£6