I'm not sure why you specifically want to make it [input random number] -> [output message], but if the [input random number] is not the important part... You

I'm not sure why you specifically want to make it [input random number] -> [output message], but if the [input random number] is not the important part... You could buy a portable digital voice recorder and pass it around the family to record their messages. This may not be as much "fun" because most probably won't have the random playback factor. To get that, you could record the messages and load them up on an MP3 player. That will enable shuffle mode. If doing some sort of custom hardware project was an important part of the idea you could wire up a permanent speaker and maybe do a 3D printed enclosure. You could take it a step further and eliminate the MP3 player and do it on a Pi with some hardware buttons. If your mum is or was into vinyl records, there are places that will custom press vinyl.