The best format is called Vector Graphics/Artwork and there a few popular image filetypes, .ai and .svg (also .dxf, .cdr)
If you are searching Etsy for something suitable make sure it mentions any of the above.
The 2nd best type is a good quality, clipart style artwork. Of these the best filetype is .PNG and least preferred is .jpg or .gif
Google Image Search
Let the search complete then hit Tools as shown over to the right
Change Color to Black & White and change Type to Clipart
Of the resulting search, the best images are solid shapes that the Laser machine can trace, cutting out and leaving the desired shape.
Best & Worst
Of these sample results, the top left are the best as they have solid unbroken artwork.
All of the others have loose pieces so the lower left, most realistic looking artwork, would actually result in several separate cutout pieces once the laser has finished cutting.