I never understood Hoppe's.
Many people swear by it, so I bought a bottle.
The stuff is like snot, it makes a mess of everything. I fail to see why so many people like it.
The best I have found it MPro7 for cleaning, because it leaves nothing behind but a clean surface. Then, I use CLP to lube and protect the parts I want to.
MPro7 is also non-toxic, and doesn't stink like large amounts of CLP does.
I use MPro7 for cleaning the bore, action, reciever, bolt, everything but the stock. I use it on my handguns too, it is even safe for cleaning powder residue off the front of polymer frames (used it exclusively on my Glock 21 and USP 9mm).
You know what I use to clean my synthetic stock on my 10/22? Spray can window cleaner from Costco. Cuts through oil and dirt well, and is safe on plastics (and metal, whatever else).
I think a coat of CLP in the bore is great, but you might want a more aggressive cleaner and a bore brush in there before using a CLP-soaked patch.