Add light and outlet to attic
So you have a keyed light (the pull chain is your switch). That likely means the power to the light is always on.

What I would do is add a double gang box below the light box. Disconnect the wire going to your light fixture (shut the breaker off first), and then wire it to an outlet. Now, run a new wire from this new box into the existing light fixture. You can buy an unkeyed fixture or just keep the keyed and stop using the pull chain. Add a light switch to the double gang and attach the neutral to the outlet, while attaching a hot shunt to your switch. Then add the wire to your light. You can then daisy chain additional lights off this light (they're generally designed to be wired in series)

Unless your attic is considered a livable space, you don't need armor clad. Armor clad is to protect wires that are exposed to high traffic areas where the wires could be damaged.