I think overall, CLP offers the best corrosion protection from my experience and what I've seen in comparison tests. For lubrication, I've found TetraGun to be very good. Ballistol is a good product, while it is stinky, from all I've heard it's entirely non-toxic and is about the least likely to adversely affect polymers or wood finishes. I've also had good luck with Corrosion-X spray. It does a good job of penetrating small orifices and doesn't attract foreign particulates. It's especially good for .22s.
Regarding Grease vs. oil, I normally take Bruce Gray's advice. Speaking of handguns in particular, he recommends using a good heavy grease like RIG+P or Slide Glide for practice and training. For carry he recommends using a good quality oil. The heavy grease affords the best protection (especially on frame rails and contact surfaces) to prevent premature wear. I don't know if he'd recommend the same for a long arm or not. So, for the 556, I just stick with Tetra oil. It's an oil that's only slightly thicker in viscosity than CLP. I still consider Breakfree CLP superior to Tetra oil for corrosion protection, so if I were in a humid environment, CLP would be the way to go.