I want to move and live in korea

A lot depends on what you would like to do and what your nationality is and whether you are a native English speaker, because the Korean authorities discriminate for ESL work in favor of North Americans, Brits, Kiwis, and Aussies.  Unless you have a Korean ethnic background, the odds are that you will get E1 or E2 visa status (teaching) or E( (non-teaching).

F2, F4, F5, F6 are mostly for ethnic Koreans(F4) or for foreigners who are married to Koreans (F5, F6, similar to a US green card).  F1 & F3 visas are for foreigners who are married to Koreans or have ties to relatives who have working visas and generally you won't be able to work with F1 and F3 status.

Most of the economic activity is in the Greater Seoul Metropolitan Area, although there are some possibilities in Busan.

The country is largely crime-free.  The country has climate similar to New York and New Jersey.  Summers are hot and humid.

What is your reason for wanting to move to Korea?

Joel