If lounge access is a top priority then 5 return flights in A or F on three-cabin aircraft would be enough to earn Oneworld Sapphire with BA. It would take 8x return trips in business (including "first" on two-cabin aircraft).

That would get you lounge access for free on any Oneworld itinerary. Not necessarily recommending that as there are reasons it's usually best to stick with the program of the airline you're flying but there are advantages the other way too.

There is a Chase BA card but I don't think offhand it would have any advantages for you. The signup bonus is pretty substantial if you start collecting Avios and want a boost though.