First question is: how would I know which data file would be best to move to the G: drive?*
Well, how would we know? I would look into if there are any databases that can permit downtime during office hours to facilitate the move. If there is no distinction that way, or such databases are too small to be worth it, I might take the database that seems to grow the fastest.
My second question is: how do I know how much space to request? Is there a simple formula I can use to calculate?
Yes, the formula is "more". No, matter how much you get., the answer is always "more".
More [sic!] seriously, this depends so much on the workload that there not a ready-made formula you can use. But from what you have told us, I say that you need at least 2TB more of disk space.