If you want to use an actual analogue phone, then you'll probably want to connect it to something using an ATA (Analogue Telephone Adapter). Modems are expecting a powered phone line which can be worked around but I wouldn't recommend it (and haven't tried it in decades and don't remember the details).
The ATA converts analogue telephone into SIP, if you then want voicemail recorded on a Pi install FreeSwitch or Asterisk as your voicemail server. The magic you want from the ATA is "Offhook Auto-Dial"; as in, when it detects the handset being picked up (going off-hook) it automagically dials a number for you - in this case your voicemail extension on your Pi based SIP server.
Unless you're specifically trying to relive the analogue days, I'd probably go digital earlier rather than later in the chain (handset to ata, rather than handset to fake phone line, to modem coopted to do something most people aren't) as it'll make things easier and make no difference to the end user.
This might not be the most elegant way, but it's the tools I'm used to using, so :\
Out of curiosity, what's the plan for the recordings after you've made them?
username[at]gmail if you need any specific advice; this sounds weird enough I'm interested and should be easy :)