A few posts upthread I have listed all OW programs' point expiration policies. With your flying patterns and given that the IAG airlines have the most generous expiration rules out there, I'd say it's a toss between BA and IB. Also, both allow using Avios plus money for tickets, which is a bonus for those who don't fly a lot but want to use their points.
You can have accounts in both programs and even transfer points back and forth between both, so that's what I recommend you do.

Also, check if there's an affiliated credit card will let you earn Avios on everyday purchases to help bolster your account and keep your points from expiring.

M&M has become practically worthless for low-spending leisure travelers. With BA/IB, your chances of sitting in a premium cabin courtesy of your points will be much higher.
The largest downsides: Ridiculously high 'fuel surcharges' (YQ) for award bookings on BA which run into hundreds of Euros for longer flights plus high taxes when flying BA via London, especially in premium cabins (IB has much lower surcharges) and no upgrades from discount economy fare classes.