Or, I could use software like AnswerMyPhone or EZVoice. If I do so, I
> will need a voice modem in my computer. Am I correct in assuming that
> most modems that come with PCs are not voice modems?
These days, most internal modems are voice modems. Consumer-grade computers often come with voicemail software. And if yours isn't a voice modem, you can probably replace it for as little as US$20.
Of course, you will need to leave your computer running, and *possibly* turn off powersaver sleep/suspend/hibernate functions (or fiddle with BIOS settings to make sure the modem can wake up the computer).