I'm trying to become a film-maker. Other than a green screen and camera, what equipment do I need?

The green screen is not needed unless you do special effects with the background. The camera is useless.

The primary requirement is a digital camcorder. You can do without the rest but if you want to improve on the quality of the images, you need auxiliary lighting. If you want better audio, a separate portable digital audio recorder would benefit you. 

From there you expand your equipment. These lists aren't complete but to give you an idea, lighting would need stands, bulbs, modifiers, bulbs, screens, bulbs, barn doors, bulbs, umbrellas, and as many watts as you can afford. Audio equipment would be recorders, mics, amplifiers, grips, poles, and more people to handle them. The camera will also need tripods, gimbals, cages, dollies, rails, cranes, remote controllers, aaarrrggghhh!!!

Lighting and the various accessories such as light stands, umbrellas or soft boxes, a snoot, grid, barn doors, reflectors, etc...

Audio recorder.

Fast computer to process your files along with a large amount of storage space not only for your main files but for your backups, too.

Video editing program like After Effects.

High-quality monitor with a calibration too like Colormunki.

Tripod

Gimbal stabilizer when hand holding the camera.

Scarlett Johansson.

You need a tripod unless you plan to shoot handheld only. You need lighting because it is too often dark indoors. 

Creativity and the longing to make it happen. The equipment is the last thing you should think about. You can also use your phone.

You don't *need* a green screen but if you're going to get one you'll need lights, and your video editor (a must have in its own right) will need to support chromakey.  You should look at tripods with a pan & tilt head and you'll need audio recording equipment.

A clapper-board.  And a folding chair.