A few things other than cost is important choosing the carrier you want to fly.One criteria is the route you want to take., if you are flying from Canada To Asia , for example, avoid going through the United States because you will have to take you luggage off the plane to have the Americans inspect it. It is really a pain in the "shoulder." Try to only make one stop and it should be in Asia.
Another criteria is how much total time it will take. You should be able to do it within 24 hours if you choose your route carefully even though it can take 30 or more hours with layovers and so on and time is of the essence, ( unless you like airport food!
Another thing to consider is which alliance you want to use because you can accumulate points quickly and you may as well use one alliance for all of your flights so you get get lunge privileges and ultimately a free trip to Asia if you want to go home for the winter break , for example.
I choose a company like Eva Air out of Taiwan because they accept two bags for free which most airlines do not. They also, by chance, upgraded me for free on my flight and I got to sleep in first class. What an unbelievable experience. The toilets were cleaned after each use, you were served your meals whenever you requested them and there seemed to be one steward for each passenger and they knew your name!
I have also been upgraded on Air Canada and had a similar experience but certainly not the same, just similar. Asians know how to pamper. So pick your airline based on cost sure, but also on service, route, number of flying hours to Asia and type of plane. You simply cannot go wrong with an Asian carrier and it will be a great way to start your adventure in teaching in Asia.