This is a question I have also wondered about and have a partial answer to. There is no audio out on the Pi Zero except via the mini HDMI connector, a problem, but not an unmanageable problem. Adafruit offers this hack for audio out via the GPIO pins :
https://learn.adafruit.com/introducing-the-raspberry-pi-zero/audio-outputs . The other approach would be to find an external USB audio card (audio out / microphone input) supported by Raspbian. As with the Pi A+ you do have the issue of just one USB port, so to support microphone input (plus possibly audio out) and some sort of network connection (wireless/wired) you will need some sort of USB hub (though it should be possible to get away with a cheap under $5 discount store USB hub). As for the the software, once the hardware issues are dealt with, it should run as the Zero has as much RAM as the model B (512 MB) and is faster (Zero 1GHz, B 700 MHz).
I do have a Raspberry Pi Zero on order, but until I get my hands on a Pi Zero I will not be able to confirm the above...