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You can use GRBL 1.1 and LaserWeb for controlling the laser. And for designing use Inkscape, all free software. ;)
If you knew what a resistor is you wouldn't ask that question...I hope i know it already... ;)
No, the resistance has nothing to do with the laser size. The resistance is there to limit the current from the Arduino pin. Just to turn on and off the laser.
You should look for the pin that usually controls de spindle. The laser is controlled by the Arduino as if it was a spindle. Your laser module should have a pin where you can connect it to the cnc shield.