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I think a Chromebook will work well for you.
First, get one with a good keyboard.
The only thing that may be touchy is fancy formatting in Word Processing but it should be covered:
In Google Docs, you can export your files as .docx (Microsoft Word format). Google Docs does have some formatting limitations. Log in before you buy using whatever you have now and see if it does what you need -- it is considered pretty decent for academic work.
There is a free (and limited) online version of Microsoft's Office Online:
Since all you really need is Word, this sounds like it will work for you. Files are saved to your OneDrive acct (also free) and can be downloaded.
You can also try ZohoWriter.com or subscribe to RollApp.com and use LibreOffice (OpenOffice). RollApp has a free option but I think the download options are limited, premium is $7 a month, Zoho is free.
A final option is to buy a Chromebook where you can install Crouton, install Linux and use LibreOffice ... although that may be a bit more work than you want for something as simple as having a good word processor. :)
Good luck. Just bought a Chromebook a few months ago (the entry level elcheapo Hisense and LOOOOVE it).