I use a few different types of steel wool on my Cooey stocks. Use the rougher one first to remove the bulk, then use a finer pad to smoothen it out. I dont bother with the checkered or detailed grips, I actually find it looks kind'uv awesome with the two tone effect. Once it feels and looks good, apply rubbing alcohol with a clean rag to clean all the fine dust off the stock and to prepare it for the final finish.
You can use a stain at this time, though in my opinion, I don't recommend it as I believe stain is for chairs and ottomans.... but I digress... I then apply a spray on clear varathane. Make sure to not over do it as the varathane will run, and leave the finish uneven. If more coats are desired, allow a couple of hours to dry before applying next coat. Takes about an hour to strip and finish an entire stock, then let dry fully for 1-2 days.
In the meantime clean all the steel of the gun with steel wool as well (if it has rust spots), and then apply oil. I don't bother with bluing as I believe it gives it an "experienced" look.
Have finished many of my Cooeys and other farmers rifles and haven't had a complaint yet. Kind of a fun job to do.
This is the only type of rifle stock I refinish in this manner though. All my milsurps get delicately cleaned with a bit of "Scrubbing Bubbles" and a lil' hot water, alcoholed and dried, then get a few coats of tung oil. Tried this method on a Cooey stock once, but it just doesn't look all that good.
Cheers!