Don't know your location, so could only guess about your phone service, didn't mention cellphone... interfacing needs more info.
For dialing the number, a microcontroller would be a good choice. Both MicroChip (PIC) and Atmel (AVR) have appnotes on their websites for generating and decode DTMF (sound you hear when you press a phone button). This would be the simplest, one chip solution.
There are some $5.00 MP3 players in the surplus market, that are fairly simple to re-purpose, you could load it to play the digits to dial, and a message.