Okay so here's what I've worked out so far. 

Aleksandra has her backstory somewhat already established thanks to what we know about Elena and the information given in BC. After the Turks left Shinra though, she's open to have either stayed with Tseng and Veld, or been moved into one of the smaller towns as a team to do surveillance, keep an ear to the ground.  I'm pretty flexible with plotting for her, though. 

For Squall, I'm going to sort of keep close to his canon background in that he's technically an orphan as far as anyone knows, graduated the Academy at 16 and was brought into the lower ranks of the Turks,  His abilities distinguished him during his first year or more and when the other Turks up and went their own way, he was one of the ones left behind.  Leadership fell to him almost automatically given the reports on how he'd comported himself as a Turk and he took on the position albeit a little unwillingly. 

He hasn't been all that effective at routing the old guard of Turks, although it's technically part of the agenda, his focus more on the happenings in Midgar and other matters than hunting his former comrades across Gaia. 

Adding Tifa, Vincent, and Two Guns to this list. Come at me with ideas