Welcome to FlyerTalk.

I think the first decision is where you will credit the miles earned by flying. Cathay Pacific is a member of OneWorld alliance. You could credit the flight to Cathay Pacific's own frequent flyer program or to any OneWorld carrier's program such as American Airlines, British Airways or to Alaska Airlines which has a separate partnership with Cathay.

To make this decision you need to know the fare code of the ticket you intend to purchase, because some programs award reduced miles, or no miles, on discounted cares.

Once you know where you intend to accumulate the flying miles it may be easier to decide how to pay.