What wiring is required for this thermostat to work — does it need a C wire?

Yes, a 24 VAC common ('C') wire is required for this thermostat to operate. The thermostat is not compatible with electric baseboard heat (120–240V) or millivolt systems. The recommended wire gauge for thermostat wiring is 18- to 22-gauge thermostat wire, and shielded cable is not required.