Thank you all for the very useful advice and information.

The AA programme is definitely the best bet for us, given that we like to visit the USA and would probably use our FF miles for trips there in the next couple of years.

Given that we are based in the UK, I still can't work out whether it would be useful to do a challenge or not. Would there be a worthwile benefit?

I have just done a quick calculation and I think if we did a challenge we would be Platinum after the PHX-DfW flight, giving us 100% extra redeemable miles for all flights after that, a total of around 30,000 extra miles each for the cost of the challenge.

Does that look right?