Short bio: Computer Scientist, FOSS supporter (read more)
Tux Machines (TM)-specific
AbiWord is a light-weight, open-source word processor that works under Linux, Mac OSX and Windows. Its layout will feel familiar to anyone who has used a word processor before, and you will find most things where you first look for them.
While AbiWord is designed to be light, it has most of the features you need, and you can add more features through its many plug-ins. Plug-ins include a wide range of import and export filters, collaboration features, a grammar checker, word definition lookup and graphics editing (using the Gimp).
AbiWord started much faster than OpenOffice.org and KWord on my computer, which had several programs open at the time, as well as playing music. I tested this both from a cold and warm start.