I don't want products to display on my website if they are out of stock, is there a way to automatically take them down when they reach zero inventory?

You can set your products to 'hide' so they are no longer visible on your website by enabling that option in your system settings. Once you are logged into the system as an administrator, in the blue bar, click on the gear-shaped button on the far right and go to Settings > Website Settings > Products and you'll see the option for Auto-Deactivate Products not far from the bottom of the list. Set it to On, and then scroll to the bottom of the page and click Save. When a product is at 0 inventory, it will no longer display on the website. Please note that it does not actually go into a Deactivated state, it is simply not going to be visible online at that point. Once a product has inventory again, it will automatically reappear.