200NL TP weak kicker in the BB

[sobos]

This a very standard hand that every player has multiple times per session. I'm wondering how different people play it.

Effective stacks=$200. Hero is 19/13/2.

Hero has A9 in the BB. 5 to the flop (unraised preflop).
Flop is A83_rainbow. Hero?

There are a few lines that I've tried out and I'm not sure which one is best. It obviously depends on the table, so please address stats when answering. Sometimes I like a B/B/CC line (against donks who I may be beating), sometimes a CF line (against a nitty table), sometimes a B/CF line (against a player who outplays me and is too smart/aggressive to outplay OOP), other times a B/BF line. Please don't respond by saying that it's case-specific; instead, state why you used each line for each case.
How does this change if the board is more coordinated? What if a shortie raises AI (how short is worth a call?)? What if it's 3-handed instead of 5-handed? What if you have AT instead? A2?