You will need to remove the nipple to properly clean your rifle but you do not need to remove the "clean out screw". Actually the term "clean out screw" is a misnomer. It is not there for cleaning your rifle, that hole was drilled when they were making the breach so they could have access to the inside of it to clean out the casting. They then plug the hole with a screw. You don't ever need to remove it.
For the first cleaning, you will need a solvent such as mineral spirits, Varsol, break cleaner on some similar solvent that will cut the grease. Then oil the outside with something like Birchwood-Casey's Barricade. Oil the inside of the cleaned lock with something like 3 in One machine oil. Use a dry rag to wipe off the stock and I like to use something like Johnson's paste wax to protect the stock. Actually, my favorite thing to use on all of the outside wood and metal is Renaissance wax. It is great stuff and is used by many museums to protect their displays.