What large-screen phone or tablet can I get my senior mother?
It’s best to go with Apple. (without getting into the iOS vs. Android debate, I think iOS is easier to use for an older person, and you don’t have to become your mother’s 24/7 Tech Support).
I would recommend the iPhone 6 with the big screen. It is straightforward to use, and she can also take photos easily. There are classes at the Apple store for first-time users too.
Another great choice would be an iPad Air 2; going for one in all devices would compromise an older adult’s usability. If apple is not to your taste, Samsung Galaxy Tab A 10.1 has one of the cleanest user interfaces out there, with highly changeable font customization and a high-quality large screen.