Based on what you've said, and for NYC, I'd be inclined to stick with Club World and save the Avios for the European trips you're planning.

Taking the A318 LCY service is a good option too (as it's the same mileage as Club World) so try to get that on one of the legs. I'd prefer to do that on the return JFK-LCY though (with lounge access at JFK and the arrivals facilities in London) unless you get BA1 on the outbound so clear US immigration on the stop in Shannon.

Alternatively, if you are really undecided, why not do F one way and J the other. You can mix and match flight classes on Avios redemptions.