Chromebooks and ChromeBoxes are locked to running Chrome OS, basically Chrome browser middleware and everything automatically linked into your Google services (Mail, Drive, Docs, etc.). They have screen reader built in called
$1 which seems to cover the basics. I'm not a screen reader user so I can't really comment. Chrome OS also has support for magnification and other accessibility feature
$1.
Although Chrome OS is a version of Debian Linux, most of the time this deeply buried and locked away. However, many Chrome OS machines can now run a bare Linux (Debian as standard) in a secure container and, if the underlying hardware is up to it, consequently run apps like Gimp and Libre Office. Most Chromebooks can also run compatible Android apps.
If you want to know more specifics about Chrome OS and what you can do with it, pop over to /r/chromeos/ where they will happily tell you a Chromebook is a bad idea for you when your requirements won't be supported well.
Cheap Chromebooks are really cheap. You could get one just to try out the accessibility than splash for a fancier model if that is what you need and can afford. If you want to run a different OS on a Chromebook it is possible but it requires opening the unit up to disable its security features, re-flash the bios and then success is not guaranteed.