1. Get a Linux shell prompt on your C64 through the Pi Zero's Console Pins.
2. Allow your C64 to access the Internet, USB, etc. wirelessly through the Pi Zero W. In particular, ssh!
3. Provide Composite Video out from the Pi Zero that is usable directly on a Commodore monitor.
4. (Stretch Goal #1) If possible - use your C64's keyboard as the keyboard on the Pi Zero (through the serial port). Maybe through softwedge? (https://github.com/theatrus/softwedge)
5. (Stretch Goal #2) Add PWM audio output (along the lines of https://learn.adafruit.com/introducing-the-raspberry-pi-zero/audio-outputs)