They are similar - but not the same, there *are* differences. Among all the programs you have mentioned, only BAEC offers accounts where you can put the miles for yourself and your wife into one account. BAEC calls this household account. If that is what you meant by "booking the miles for both tickets". If you meant just that you want to put you QF and BA miles in one program - any OW FFP will do as "B" fares should earn full mileage anywhere.

This trip is less than 28,000 miles all in all and will not generate enough miles/tier points to grant you OW Sapphire status (which will give you lounge access - you'll need 600 TPs in BAEC or 50k miles in all other OW programs to qualify for it) on its own as far as I can see - but calculate for yourself with the tier points calculator on BA's website. So unless you join BAEC now and plan on doing some regular flying before starting this trip, you're out of luck.
Upgrading LAX-LHR: Pretty much the only realistic chance to get an upgrade on that flight is when you stick with BAEC and use Avios plus money (calculator here). Make sure you upgrade into Club World ('CW', business class), not into World Traveller Plus ('WT+', Premium Economy). The upgrade into WT+ costs only half the Avios, but the experience is not much different from economy apart from a slightly better seat. CW will give you a true premium cabin experience with lie-flat seats and nice food. Plus a CW ticket comes with lounge access .

In a nutshell: Enrol you and your wife in BA's Executive Club, and redeem as many of the miles (Avios) you earned on that trip as possible towards upgrading the LAX-LHR leg. You might make this without the co-pay when you take out a BA credit card: The better of two cards BA touts comes with a 20,000 Avios sign-up bonus (I presume you live in Germany, here's more details).