The quantity textfield on an Add to Cart form can be turned off in the display formatter settings for the product reference field configured to display the form. It defaults to not display, so I assume you started building your site using Kickstart 2.x. Whether you are or not, though, these steps should still get you to the form to turn it off:

1. Browse to admin/structure/types.
2. Click the "manage display" link for the product display node type you're using to display your art products.
3. Locate the row for the product reference field using the Add to Cart form display formatter (called Product variations in Kickstart 2.x)
4. Look in the settings summary to see if it says "Quantity widget: Enabled". If so, click the gear, disable it, click the Update button, and then click the Save button at the bottom of the page.
5. Repeat the process for every view mode seen in the secondary task tabs area (Default, Full content, Teaser, etc.).

In your case, once a product is sold, you can use Rules to disable the product so it will no longer be purchasable. It will still be visible in product displays, but the Add to Cart button will be disabled.