Most any modern-day PC will operate your laser. What you choose is based on the graphics software (and perhaps other software and attached hardware) you need/want. If you plan to process large graphic files, a memory of 16 GB or larger with a fast processor and high-quality graphics card saves you time and provides the best results. PCs designed for gaming work well, as the specifications are similar to working with graphics.
The two most popular basic graphics programs for the awards and customizations industry are CorelDRAW Graphics Suite and Adobe Illustrator and Photoshop. Other task-oriented software available that are useful as well. A few include PhotoGrav for preparing photos for laser engraving, PhotoScissors for removing backgrounds or objects from a photo, and Graphic Tracer for turning bitmaps into vector art.