One issue with AA's AAdvantage program is that BA's transatlantic flights do not earn any qualifying miles in spite of AA and BA being in the same alliance (OW). And BA's program is probably even stingier.

If lounge access is a big factor, you probably want either *A or OW, as ST provides lounge access only for the top tier, and then only for international flights; *A and OW give access at the middle tier. Within *A, UA and US also limit each other's members' access on domestic flights, but non-UA/US *Gold members do have access.

Given that, one suggestion to consider would be AC, even if you primarily fly other *A members. AC's mid-tier starts at just 35K, and gets you full *A lounge access. For the TATL/TPAC upgrades, though, you might need to route through YYZ, YUL or YVR.