I am relatively fresh to the xcom world- enemy unknown being my only personal experience- but i have to admit to having created backstories and personalities for my squad on many an occasion, even going so far as to have their personalities impact how I played them as I immersed myself in the conflicts xD

Character driven and combat oriented can indeed go hand in hand; detailing our character's lives as they relax at HQ- just to suddenly be whisked away to an abduction/assault at a moment's notice!

As for setting- my only personal experience would be 'enemy unknown', so 'near future' is an admirable outcome- but I'm fine with researching any necessary information should the need arise.

As for starting point- my personal preference Always leads to as far before a key conflict as possible; Recruitment/training. It allows for adequete character development whilst allowing for the suddeness of an alien invasion to spur on further development and changes-- however, it is understandable if many wish to skip this. I have no single preferance for this, but if i had to place a vote it'd be 'at xcom before any major event' just for the sake of skipping possibly tedious (for others) recruitment/training situations.

Naturally, i'd be fine with whatever is decided- but that's just my little perspective