I'm going to assume that you want to buy a new phone. Having said that, there really is only one phone that fits in your price range and more or less meets all of your requirements
The Moto G
I would strongly recommend this phone over all others. If you're a fan of smartphone literature (ie keep up on all the news and what not), this is the ONLY phone that is in the conversation at all with regards to sub $250 phones. Otherwise the media only talks about the $700+ flagship phones.
So yeah; this is also the recommendation fo pretty much the entire android journalistic community: buy the Moto G
Of course that's only if you want to go with android; Nokia offers some very good Windows phones that also meet all of your requirements in a similar prices range. Check out the Lumia 730
Actually after checking out the Lumia 730, it seems like a very tempting buy.
With regard to your mother: if she's willing to bump her price range up a little bit, I'd recommend her to buy the Nexus 5. Even though its a year old and Google still hasn't knocked its price down, I still think it offers the best bang for its buck compared to anything (possibly with the exception of the 1+1).
Hope that helps