i would like recommendations on which airline should i travel with to go to South Korea?

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Without knowing your departure point, I think nobody will be able to provide you accurate suggestions. BTW, What are you looking for? The cheapest airline? The airline with best service?...

Well, that would be via Europe or the US West coast, then.
I like Asiana, but I'm pretty sure some US-based Airlines go here too.

If you depart from Miami (and probably if you depart from other points in Florida), the easiest option would be with Delta (or a mix of Delta and Korean Air) changing planes in one of Delta's hubs in the USA. Take a look at the web of Delta to look for fares.
