We recently bought a Doro Secure 580 mobile phone to support a member of staff who is unable to read. It cost £83 from Expansys including postage and seems to be ideal for what is needed
It has a plastic door on the front, behind which you can put a list of up to four names, or even tiny photos. Holding A, B, C or D for a few seconds calls the corresponding person on your list (or you can tap A, B, C or D then press the green dial button).
There's a panic button on the back of the phone, that can sound an alarm, and call from a list of up to five emergency contact numbers until you get through. It can be disabled.
You can also assign a "whitelist" of trusted callers. If anyone calls who is on that list, you'll get the call. If anyone calls who is not, they'll be blocked. This can stop people being approached by cold-callers.
It comes with a charging cradle and neck strap, quite a few ring-tones to choose from, and is unlocked to any network. Nice phone.