What is the best/cheapest way to fly between Asia and Los Angeles?

I am planning to fly to Los Angeles from either Bangkok or Singapore next January. What is the best way to do this and are there any budget carriers that fly this route? Does flying between Asia and the U.S require a stopover in either Japan or Taiwan/Taipei or can you fly direct from Singapore/Bangkok?

The best way is not the cheapest. The cheapest way is never the best. Please make up your mind if you want best or cheap.

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Try Thai Airways or Malaysian Airlines