She has two choices, really.
A dvd recorder which works in exactly the same way as a video recorder, except you use dvds instead of video cassettes.
The basic recordings are pretty the same as the VCR and she can ignore the fancier facilities.
Or she could get a PVR. This is a hard disc recorder, so no removable dvds to mess about with. Usually you turn them on, bring up the programme guide (one button), use the arrows to find the programme you want, press the record button and that's it. (Very easy to set it to record the series too, with one button).
Very easy to play back the programme, from a clear index of stored recordings. Really very easy.
The advantages of the dvd recorder are they are cheap and the recordings can be played in most dvd players. It will play shop bought dvds too. You can keep the recordings for ever, if you want to.
The PVR is more expensive, but if it has two tuners you can record two programmes at the same time, or record one whilst watching a recording. No dvds to mess with and hunt through to find a particular recording.
I have a PVR with a dvd recorder attached to it so if I want to keep a recording I can transfer it to the dvd .
The most important thing is to make sure the recorder has it's own digital tuner, then she can watch a different programme on the tv while recording and she won't need to keep the tv turned on to record.
If you decide on a PVR Humax have a good reputation. This one has a large hard drive.
http://www.amazon.co....n-Tuner/dp/B00272N9PC