I just have it in the same case as the mobo using the port at the bottom so dont have to use the external side and make mess outside the case.
Yes connecting the green cable to any black one on a PSU will make it start up so might be best to rig that up to a standard on/off switch (not a PC case one, you need one that is either on or off not momentary) so you can power it up neatly rather than say using a small length of cable.
I will be shortly rigging up a 40mm fan to blow over it though as it does still use 11 watts of power so don't want it getting too warm