I would be careful about putting too much emphasis on what fleet you end up on. Yes, if you’ve got 20yrs in SH outside BA and want a change it’s important, however if you’re near the beginning of your airline career, getting lots of sectors and handling doesn’t hurt. I really enjoyed my time in SH, but moved on to LH which is more suitable to my lifestyle - YMMV.
Also, the next ten years will see a lot of movement internally as the bulge of those recruited in the late 80s and early 90s retire. Even without any expansion, there will be many empty seats to fill at the pointy end on all the fleets, LH especially. There should be plenty of opportunity to bid for and achieve postings other than your fleet of joining.
As far as route networks go the 777/787/A350 all have a decent choice of destinations, 777 the most as it includes LGW leisure. The good news for all is that there is a fair amount of seasonal variation and substitution between the fleets, so quite a few destinations move around and everyone gets a go. The A380 will always be a bit limited, but being on what BA terms a “small fleet” can have its own advantages.
In reality, you can have a good time anywhere, and it’s about the people you fly with that make the difficult days more bearable, and in my experience that’s pretty much everybody.