BA and IB's programs are practically identical. They use the same 'currency' and you can transfer points between accounts between both airlines as well. IB doesn't charge the outrageous YQ surcharges for award tickets BA does.

As you have noted yourself, your main concern as a not-really-frequent flyer is keeping your miles from expiring. BA/IB have the most generous expiration policies out there (check a few posts upthread, I've listed them all there. I think a lot of what's said there pertains to you as well).

QF miles expire after 18 months with no activity - I have no idea how their non-flying earning options are for European members.
While AA is indeed a solid program and I'm very happy with it, there's two things that I'd keep in mind: First, most of the "extending miles with minor purchases" options that AAdvantage offers are limited to US-based members. The AAdvantage shopping portal as well as the dining program are geared towards US residents and don't have many or no European partners. Miles gained through hotel stays and car rentals (all major international chains are partners) are your best options here.
Second, looking at AA's US competition and what they have done to their FFPs recently (devaluations galore) and what with AA and US merging their FFP in the next year or two, I'd be careful about starting out with them right now.

Your home airport listing suggests you live in Germany. The easiest way to earn non-flying miles in any FFP is with a co-branded airline credit card. BA offers one in Germany with up to 20k Avios sign-on bonus (link). AA has one on offer as well, but is way less generous.