Earlier often seems to be better, but it's hard to predict fares. Some of the general booking sites like Kayak attempt to estimate if a given fare will go up or down.
Your options are more than American or United, you will very likely wind up on a mix of airlines and you'll want to play around and see what is available. I don't think American even flies to Manila itself, through them you would be on a codeshare with a partner airline such as JAL. United flies to Manila or did, but their schedule isn't great and they don't have much of a presence there. But they also have partners that fly there, such as ANA. Or you might just wind up hopping to someplace like Houston or LA and taking some other airline. Philippines Air direct from LAX would be a common route and sometimes the best deal, but they're not partners with any particularly useful major US airlines. Philippines Air does run some pretty good deals - far in advance may work, or catching one of their periodic fare sales is good, but I don't know if there is any usual schedule to when the sales happen.
You could also check if it makes sense to fly into Cebu from the US, which they seem to be trying to expand as a second international airport. Fewer flights than Manila but it might be more civilized if it works out. (Manila is over capacity and can be a mess. If you can avoid changing terminals between your international and domestic flights it's a good thing, though that part has improved somewhat. They have 5 unconnected terminals and you can lookup which airlines use which. If you decide to stay overnight in Manila then of course it doesn't matter.) If you're ending your trip in Anilao obviously you'd leave from Manila, but it's possible the open jaw thing won't hurt you on price.