BA is not very good for earning miles or status flying economy, and due to the AA/BA rule there is no earning on AA trans-atlantic crediting to BA.

AA is probably best for you. Decent awards. You're at a one world hub. If you get status on AA then you can use status benefits even when cashing in BA miles on an award. But for that you really need to be platinum (or executive platinum).

If you credit all your hotel, rental cars and credit card points to AA then they all count towards lifetime status (lifetime gold at 1 million miles). Very few other programs include these non-flying earnings as a way to get lifetime status.