Mary's mother in law is almost totally blind and she's wanting to get a phone with big buttons and enough storage. It also needs a voicemail feature. Leo says that most of the time, carriers have voicemail service. Any phone with a keyboard will likely have a button dedicated to activating voicemail with a touch of a button. But they don't want a cellphone, they want a landline phone with a built-in message machine.
Companies that make phones with big buttons include Big Button, with large buttons, screen, and has an answering machine. AT&T sells one. Check out Independent Living Aids. Clarity is designed for the blind and people with macular degeneration.