Since you'll be in economy, I recommend choosing the cheapest non-stop flight or the least inefficient 1-stop flight. As you don't fly much, earning miles and status isn't one of your big concerns, so the carrier won't much matter.

Honestly, the flight is only 14 hours or so (IIRC), so even in an uncomfortable seat, it won't be that bad. If I were to choose, I'd definitely go for SQ first, followed by UA (Yes, I know, I know...). I have had a couple of fairly unpleasant flights on CX, so I have something of a vendetta against them.