A couple of years ago, I was also looking for such a package. I had a physical fax machine, answering machine, and PC with a modem. I had to try...

I tried vgetty and found it did what I wanted: automatically answer the phone (a) play back a greeting and record a message or (b) switch to receive a fax. It could also switch to become a data line but I never tried using that functionality. This worked fine under both Linux (RH) and FreeBSD with an ISA USR voice/fax/data modem.

Some problems I encountered:
- voice recordings incoming and outgoing were in a proprietary format. Tools to convert to/from that format existed and were relatively straightforward to use/script but made editing sound clips more difficult.
- greetings needed to be recorded in the propriety format. Phoning myself from my cell phone and copying my recorded message avoided having to do audio conversions.
- WAV files after conversion were 100s of KB for even short messages. Converting messages to MP3 (LAME encoder with voice settings) made them small
- checking messages remotely was easy once the MP3 files were exported to my web server in a password protected directory. The same browser could also check faxes.

Good points too:
- I was receiving an annoying number of junk faxes. At least now they did not use paper and could be easily deleted
- being able to attach a received fax to an email message and forward it on without using a scanner was neat

Didn't try:
- checking messages remotely with voice commands or touchtones, but I only got as far as the documentation. I used a browser to check messages/faxes.
- I think it could also work with caller id to screen calls

However, after several months, I went back to an inexpensive, battery-backed, touchtone remote controlled, dedicated answering machine and connected it to the real fax machine. It was just easier to use and maintain.