Hello @AdrienneWattsAr thanks for your post. I think there are some sellers that have set up self-serve kiosks in their businesses...mostly likely using an ipad setup. I'm just personally worried about your studio setup you mention...as an artist myself I just may not be understanding your setup correctly...Would people be entering into a studio that is un-attended, and then self checkout, and then physically take down the artwork off of the wall? Personally, I'd just be concerned about having a customer do that, but maybe your artwork pieces are small and not heavy?
If you didn't want to use an ipad setup for a kiosk setup, the easiest way I can think of is to create individual checkout links. When you go into your Square online dashboard, you can create a checkout link for each item. See this post with some info about this. You can then generate a QR code that you could printout and affix under each piece of artwork. The customer would scan the QR code with their smartphone, pay with the checkout link, and then take the artwork. I hope this might help achieve what you're trying to accomplish.
