Do you have experience in Tex or are you learning?
Recently, I wanted to learn as well, and since I use Arch Linux I followed these:
http://wiki.archlinux.org/index.php/Category:TeX_(English)
http://wiki.archlinux.org/index.php/LaTeX
They have the Tex Live distribution.
For an editor, I installed TexMaker. Looks nice. It has a Windows version as well.
http://www.xm1math.net/texmaker/
BTW, you mentioned mingw and Cygwin, have you seen andLinux?
http://www.andlinux.org/