The electric choke is easiest adjusted when the car is at ambient temperature. Just a light nudge off idle position, and adjust the choke to fully closed. If the windshield wiper or whatever its hooked to is powered up when the key is on, then yes, turn the key off. Now the adjustment wont be just til its closed. It will likely need a little more than that. I'd adjust to fully closed at ambient temp, then give it a slight amount more. Tighten it up, reattach the power wire, and start the engine. You'll be able to tell if you need a little more or less choke, and adjust accordingly. I'd suggest locating a better power source than the windshield wiper circuit.
This is all assuming that the choke will turn in the housing when the 3 screws are loosened. If it will not move, you must find out why. Theres not a lot that can go wrong with that component.