AA and One World would certainly work from SFO, but bear in mind SFO is not a hub for AA, so you'll find more nonstop UA destinations from here than you would AA which serves just its hubs (LAX, DFW, MIA, JFK, ORD, and the former US hubs at PHX, CLT and PHL).

Qantas just restarted SFO-SYD the week before Christmas (747-400), though only five days a week to start. I know it's up to six days a week by at least May when I'm flying in business. They have other Australia flights from LAX (A380 and 747 service).

None of AA's partners fly nonstop SFO-SIN though you could probably find a route with Cathay or JAL via HKG/NRT/HND that works with the same one-stop you'd have on UA. Take a look at the One World timetable for ideas:
https://www.oneworld.com/

BA flies SFO-LHR. I was just on them two weeks ago coming home from Amsterdam. If you want to go on AA metal to LHR you'd have to jump down to LAX which operates the newish 777-300 (my favorite AA aircraft right now, used primarily on flights to SYD, SAO and LAX-JFK-LHR), or go via a different hub. Here's the business class seat on it:


Just a matter of how much you value nonstop flights versus connecting. I have photos of some of the Qantas and AA aircraft linked below.

One thing you'll need to look at is AA's frequent flyer program which is changing this year to see how those partner flights accrue in the new program. AA has been very good to me over the years with domestic upgrades averaging around 90% the last two years and only one missed international upgrade in 14 years (HKG-DFW last October). If you're not on AA metal for international, though, those systemwide upgrades won't be of any value to you.