When budget comes in to play, while I've never had one my understanding is that if you're looking for something in the "get online and do word processing" range you can't really beat a Chromebook. I think on the high end those are running about $300 (personally I would peg anything under $400 as being in the "budget" range for a laptop). Chromebooks also apparently already come with some built in speech-to-text functionality, although I suspect you'll have to provide your own microphone -
http://www.techrepublic.com/article/pro-tip-how-to-speech-to-text-in-google-docs/Of course, the caveat being that a Chromebook is essentially a brick if you lack internet connectivity. Although I have also heard that complaint is fading somewhat as they are becoming more capable - although not on the level of a normal laptop - of operating offline.
As far as more traditional laptops if you do want offline connectivity, I'm actually a big fan of ASUS as a brand - they've been by far my most stable laptops and can give you a bit of bang for the buck.
I don't feel like this would be a bad buy, for instance -
http://www.microcenter.com/product/455711/R556LA-MH31%28WX%29_156_Laptop_Computer_-_BlackLaptops are nice in the sense that you do see (more or less) a pretty clear ascent within a brand. If you were only looking at ASUS computers, the more they cost, the more you expect to get in processing power, storage, or other bells & whistles (albeit some you might not need). For simple everyday usage this is probably all the power you'd ever really have to make use of.
My only other advice would be to maybe go into a store such as a Best Buy if you have time and actually compare a few monitor sizes so you can get an idea of what you're looking for. I don't think I could personally recommend a monitor smaller than 15", but your friend might have different needs. And arguably a bigger monitor should equate to a bigger laptop body, which should mean more space for a fuller keyboard - which could be useful versus trying to operate with limited movement on one side on a tiny keyboard if they don't want to use the speech to text all the time.