Wow, thanks to everyone for this welter of information & for the welcomes. I'm incredibly grateful. I think this is the most effusive forum I've ever had the pleasure to interact with. (tho I struggled mightily with all the acronyms, which fly so easily off everyone's expert tongues).

@irishguy28: thanks for the update on BA/AA anti-trust -- good to know!

Thank you to vla, Camflyer, dnajockey & others for specific flight insight -- I'm sure you have saved me a couple of miserable route acclimatization trips right there

My take-homes from all your feedback are (if I have got anything wrong do correct me) broadly:
1) AA beats BA for award flights redemption and status flexibility
2) BA beats AA for joint points earning, lounge access

I am, at this point, inclining slightly to AA, because as Jenbel and Crystak point out, upgrading and redemption in AA are cheaper, and that's more important to me right now than cabin comfort. (Also I am like 5" and all airline seats seem fairly decently sized to me). I'll also, because of my job (research) be travelling a lot, and doing the Platinum challenge seems entirely feasible.

But I have one question which might be totally dumb: if both AA and BA are One World carriers, why are their points in competition? By definition, aren't OW miles open to all airlines in the alliance? Can I not convert BA miles into AA miles, by e.g. earning BA miles in the UK with Tesco and BA Amex and then converting those into AA miles, which I can amp up by getting status through the challenge, and use to redeem flights?

I also wonder: what are your thoughts on which--AA or BA--is just straight up the a) better and b) cheaper airline? I do plan to travel cheaply, and lounge access at this point is a nice-to-have rather than must-have. I guess the upshot is: If I were to buy a cheap economy flight with either BA or AA, which would move me closer towards my goal of maximizing flights for money spent? How about if I were willing to shell out a bit more (but how much?) if it would make a substantial difference? Jimmie76's suggestion is compelling in this regard.

Oh, and I'm female!