Interesting timing. I just spent most of the day hooking up Notepad++ to MiKTeX for my Windows machine. It was fairly involved but I like the result. I think one consideration to contemplate is what else you do with computers. If your project will involve any programming or other analysis, then you may want to chose an editor that you can use for those other aspects. That way, the time you spend learning the editor will help with multiple aspects of your project. Of course, this is true for vi or emacs as well as Notepad++.
The complexity on the front end should be made up for by simplicity on the back end. Plus, it's free. The only thing that doesn't seem to be working exactly right is the forward and inverse search highlighting (clicking in the pdf to highlight the corresponding source line and vice versa).
Bruer's blog discusses the advantages at length but in a nutshell, Notepad++ is a remarkably full-featured, lightweight text editor for Windows, especially for a free one. I suppose programmers will generally appreciate it the most since it provides syntax highlighting and auto-complete functionality. Bruer's blog provides utility files and full instructions for getting the system set-up to work with a lightweight, free, pdf viewer called SumatraPDF. Finally, while it can be set up to work with various LaTeX implementaitons, he recommends MiKTeX which seems like one of the most popular for windows.
The setup for Notepad++ while a little complicated, amounts to a simple intro to some of Notepads higher level functions like macros.
So, it boils down to:
Notepad++ -> MiKTeX -> SumatraPDF
editor, since this is a matter of taste. For an absolute beginner of Windows, I would suggest TeXMaker
TeX Liveit brings TeXworks, an editor I really like. What I can recommend you is to use a shortcut expander such as
Autohotkeyas it will save you a lot of time. See uweziegenhagen.de/?p=1517 for a few examples (in German)