How do you wire and replace an old bathroom vanity light fixture
Not all fixtures need junction boxes. Some fixtures have a built-in junction box like florescent light fixtures or bathroom fan/light combination fixtures, so it will depend on what you're putting up there. If one is needed, then you're correct with your plan. Turn off the breaker that controls the circuit. You'd want a metal old work box and would connect your armored cable to with with the connector from your old fixture. Test you wires for voltage, 120V, black to white and black to the armored shield, which would mean the armored cable is grounded. Make your fixture connections and mount it to the junction box. Turn on the breaker and flip your light switch.