Actually I wound up going a totally different route after pinching the **** out of myself and filling the room with shrapnel a couple of times. 
For the lightweight materials, I created a cheap “sticky” mat to hold the little bits and pieces in place while they are being lasered. Just a sheet of scrap plywood with a couple of coats of Krylon #7020 Repositionable Adhesive spray. Works like a dream. (Or you can buy a Seklema mat for about $80).
For the heavier stuff like wood - it generally doesn’t shift unless it’s a smaller piece, but the Honeycomb Pins shared here are fantastic, and I like them better than taping down or using magnets. You can cut a few once you get the machine.
Some of the other guys use magnets exclusively though. They can tell you what works best.