I'm probably the wrong person to anwser, because I have no experience in Korean or CJK usage in latex, but if you "only" want to typeset Korean and (maybe) latin texts, I would suggest to use lualatex (or xelatex). The benefit is that those latex engines are build to use the UTF-8 encoding without any hacks and they support OTF fonts. So you can use any system font you have to typeset your document. Here is a small example:
% !TEX TS-program = lualatex
\documentclass{article}
\usepackage{fontspec}
\setmainfont{Batang}
\setsansfont{Dotum}
\begin{document}
testing 안녕
{\sffamily testing 안녕}
\end{document}
Here I use the fonts Batang and Dotum shipped with Windows, but you can take any other that have Korean characters support. You probably know some of them. If you do not like the Latin letters you can also define commands to switch to the desired font:
% !TEX TS-program = lualatex
\documentclass{article}
\usepackage{fontspec}
%\setmainfont{Batang}
% or
\setmainfont{TeX Gyre Schola}
\setsansfont{TeX Gyre Heros}
\newfontfamily\dotum{Dotum}
\newfontfamily\batang{Batang}
\begin{document}
testing \batang 안녕
{\sffamily testing \dotum 안녕}
\end{document}
If you have predominantly Korean text you can of course define font commands for the latin text and use the Korean font as default. I hope I could give you a starting point.
hangul.sty
package is on CTAN.