You will not need any headsets. They are provided, and CX does not allow you to use your own headset anyway. The planes use a one plug headset and some of the freighters use ANR headsets which are pretty nice. The pax. and some BCFs use these really crappy ones.
I believe the only things you are required to bring are a calculator, a pen, and I think a flashlight? So, if you wanted to, you wouldn't need a bag. Having said that, most people carry around a laptop, so you will see most traveling with laptop cases. You won't be lugging arround any bulky manuals, so the old square flight kit bag is way oversized for this task.