By both the common current common informal usage (of relatively developed economies) and the original definition (nations allied with the US in the Cold War), South Korea is a first world country.
Because it wasn't an economic criteria, you've also got countries like Angola in the First World by the original defintion.
No, you didn't. Angola was never both a country and part of the First World (Portugal was part of the First World when the term was coined, and Angola was part of Portugal then; when Angola became independent, the regime was Cuban-backed and Soviet-allied, and thus it was part of the Second World.)
Not only is that wrong (the Republic of Korea was and is about as closely aligned with the U.S. as a country can possibly be), but it's confusing, since what was clearly meant in the context of this thread was the different, colloquial meaning of "1st world" meaning "developed" and "3rd world" meaning poor.
Regardless, SK is unambiguously 1st world according to either definition.
edit: Apologies, looks like I was completely wrong since the source online I looked at incorrectly defined SK as economically undeveloped (I looked further and SK is in the G20, which would clearly make it a developed nation), and I was unaware of the Cold War era designation that commenters have pointed out to me.
I was always confused why SK would be considered a 3rd world country when my own impression from its industrial strength was that it should be a 1st world country, so I'm glad that I've been corrected.