As others have said, if you need the engraved plastic, then a trophy store is a good place to go. The one I go to does everything from pin-on name badges to large placards.
But, if there is a reason why you prefer having your own machine, then looking at a label printer may be the better option. The number and types of labeling materials have expanded greatly over the past few years, and you can get some incredibly strong and tough labeling supplies. Plus, there are vendors who will give you a label printer free when you buy supplies. That cuts the costs tremendously. In addition, a good label printer can be used to do many other labeling and sign making jobs. And a good label printer will come with free database software that will keep a record of your arc flash labels.