Wheather your stock is laquered or oiled will have a result on the finnish you aquire.
If its laquered then you can sand it back, prime it with a couple of coats, paint it then finnish it with a good laquer or varnish. Giving you a paint job that will last and take some abuse.
If its oiled the likeleyhood is that your paint will blemish as you may not get a good bond to the greasy woodwork. Over time the paint will lift and flake and as moisture gets in it will only get worse.
Removing the laquer from the chequering will take the use of a good paint stripper, if you sand it you will r