The few times I've removed checkering for a plain finish, it was with a palm sander and 80 grit sandpaper. This is a very aggressive combination so you'd want to be paying close attention to how fast the material is coming off. Finish up by moving through the various grits and finish up with about 320 or 360 grit.
Also, stay away from the wood to metal portions until the very last bit of sanding. That part is best done by hand anyway.
Depending on the gun, the checkering is fairly deep and removal will significantly affect the lines of the stock so you need to remove material from the rest of the stock to keep the lines clean and straight. Leave the buttplate on and sand it together with the stock.