The resolution of an image matters. You can not take an image that is for example 72DPI and make it 250DPI and improve the resolution. You need to start with the higher resolution to get good results from the laser engraving. Most images on the web are 72DPI.
If you look at your business card or letter head the logo looks good. But take a look with a magnifying glass or try to copy it and the low resolution and the fibers effect the quality of the scanned image.
The original art work is always the best, either a digital file or a high quality image for us to scan in on glossy paper, full size or larger ( detail and quality may suffer if we need to enlarge the image) and a resolution of at least 250 DPI.