I was there last year!
It's probably going to depend on where you're flying from but for me the cheapest Airline when going to Asia has always been Air China and the quality in economy is the same as any other Airline.
Their app kinda sucks and the carry on weight limit is really low but that's the only drawback while tickets are sometimes half the price of others.
I usually use a comparison website like Momondo to find a ticket and then I go to the airlines own page to book it so there's no inbetween, I also recommend browsing sites like that in incognito because some are known to dynamically scale prices after tracking what you are looking for.
If you are going to Tokyo you probably want to go for Narita Airport.