Can I get AA miles when flying BA?

Not when flying a BA transatlantic route between the US and the UK. You have to go up to Canada and fly BA's YYZ-LHR, YVR-LHR, etc. routes to earn AA miles.

You can earn AAdvantage miles when flying on the rest of BA's system, AFAIK... e.g. within Europe, LHR-Asia/Africa, etc.

kimah, you seem to be happy to research pretty thoroughly - one site that has a huge amount of relevant info is ANDREWCX's Frequent Flyer Resources, especially the credit card comparison section - that'll give you all the caps & costs so you can make informed decisions on credit cards.

His whole site has heaps of up-to-date information on general frequent flyer stuff too and it's worth checking all the tips and remarks as well. It should help a lot in your planning.

Good luck with your trip :)

hmc

Wow! What a great site - how could I have missed that? I love all this information - I've gotten so much off of Gary's website, too. It's been a tremendous help to me. Now I know what I'm going to be reading the rest of the night :).

I know it's heresy to suggest this here, but given how infrequently you fly, unless you run huge credit card tabs each month (personal or business), IMO your best bet would be to try to book 2 or 3 FF seats and use $$ for the others -- and have the $$ seats be for whoever in the family flies the most (so they keep building more miles). A Europe trip can easily generate 10k FF miles, which puts you on the road toward the next trip...and to status, but that's a whole other topic!