Congratulations on the 10/22. I don't do anything in particular to clean them. I almost never do anything to barrel. Leave it alone. I clean what I can reach through the ejection port with a Q-tip and some Hoppes. I put a drop of whatever gun oil I happen to have laying around from time to time, and call it good. Wipe it off with a silicone cloth, and that's it.
For God so loved the world that He gave His only begotten Son, that whoever believes in Him would not perish, but have everlasting life.
John 3:16 (NKJV)