i would prioritise
smart tv or include chromecast/roku in budget...if shes a skype user then its a big benefit to take make/calls in the living room. Smart tv is typically simpler to use/support for parent...Samsung probably lead in software area. Web browsing on TV is also very useful for some, test browser support and performance on favourite websites. wifi may be important if running a cable (much preferred) is not possible.
Consider requirement/Test PVR Performance(/Compression)...recording to usb/hdd can be very useful and cheap and simple.
Consider how many inputs your going to need.
Test them out in person in store, there is a lot of guff/marketting features that make little difference to real world use. But also things behind the scenes that are difficult to percieve eg web browsing performance.
Picture quality is not usually an issue above complete budget apart from die hard av fans, but seeing in person can also confirm this.
Id value warranty very highly.
4K is not critical, like for like id value it as +20% cost due to only piece of mind, content is not widely available, and even less important on small tv sizes.
3D is a non issue/gimmick spend the money on something else.
id start with samsung for a smart tvs, but if not required, id start with sony/panasonic for a trusted brand in tvs.