Is this SSR a good choice for switching 16V AC/~8mA with an Arduino?
It might work, but it's not designed to work at such a low voltage. The zero crossing inhibit is as much as 35V which means it could never trigger at all from a 16VAC source (22V peak). It is typically about 12V so it could just work badly. 

I suggest using a MOSFET output SSR such as the Toshiba TLP2222A



The LED needs ~7.5mA at ~1.15V so a series resistor of about 240 ohms is probably about right- not sure what the voltage drop is of that chip so you might want to check the voltage across the resistor to make sure the current is high enough.