Joey,
Welcome to FT!
Yes, AA miles do expire after 18 months, but you can extend their validity by even the tiniest of activity on your AA account. This could be by a short BA flight or even some kind of non-flight transaction (e.g. online shopping, restaurant meals etc).
The 'best' program really depends on your personal criteria, but do check which carriers charge ticketing fees (and how much) or fuel surcharges for award tickets. Of course they keep moving the goal post all the time, but that is another story altogeter!