OpenOffice is dead. Don't recommend it.
Use LibreOffice instead.
I did a little work on PyRoom way back when. I rather like FocusWriter.
If you're using Linux, then a program my brother helped developing, called "pyroom", may be the perfect solution for you (in case you want to write your texts on a computer.)
Here's a link to the features and a screenshot on the homepage. http://pyroom.org/features.html
Pyroom enables you to write distraction-free, because it runs fullscreen and blocks, or leaves out, everything that may distract you from the writing process (buttons, popups, other programms, ...)
I would definitely suggest Pyroom, simple and fullscreen. The best part is the themes. Whenever I get sick of the screen I just switch to a fresh theme.
http://pyroom.org/ if you are interested (it's free)
I bought an IBM T41 laptop with no wireless card, leaving me with no possibility of internet, unless I go sit behind my bookshelf and couch where my router is. I installed Ubuntu and pyRoom for 'distraction free writing'. Sometimes I listen to music. Classical, mostly, or stuff like Philip Glass's Sole Piano.
This really depends on what type of text you're editing and how much time you're willing to invest in learning a new tool. If you're editing structured text like source code (or even markup languages like markdown, latex etc) vim or emacs are great choices because of their flexibility and programmability. But both come with a steep learning curve and are not very intuitive for those coming from notepad in Windows (vim -y is a an option that simulates notepad though). Otherwise some options are nano, micro, leafpad, gedit, kate etc. If you don't find micro in the package manager it can be downloaded from the link (there's nothing to install just an executable), it is worth checking out.
If you're just writing unstructured text (like prose) probably gedit or leafpad is the way to go. Two other editors that offer distractionless editing are pyroom and focuswriter. Both should be available in the repository.