Smartphone for my grandparents

[TheNH7]

Hey people!
Recently both my grandparents' cell phones (some old Nokia shells) started falling apart and after several months of arguing they finally agreed that we'll get them a smartphone.
Been researching for a while (not too familiar with the low-end stuff) and I've kind of settled in to the thought of getting them both a Samsung Galaxy S3 Mini (for the 1500mAh battery and hopefully small yet not too small screen size) but I'm not entirely certain.
Looking to spend around 200$ (in local currency) and I'm looking for an Android device with a ~4" screen, the more battery the better and version 4.2 or newer (preferably without rooting and switching roms because A. I don't have too much time on my hands and B. Would probably void the warranty that they might need)
Also - any suggestion for a better UI that could ease the switch and assist them? 
Thanks!

[HmmR]

1.moto e

2.moto g or

3.red mi 1s

 

are the best budget phones

[TheNH7]

1.moto e

2.moto g or

3.red mi 1s

 

are the best budget phones

 

The Moto G could be pretty good but it's slightly out of my price range and I think they'll be more comfortable with a smaller screen size. Can't find the Moto E here for some reason and for the Redmi I think the 4.7" screen is going to be too big and yet again, out of my price (unless I'll order from china, which is not likely since if something happens RMA is going to take ages) 

Any other suggestions?