Since RIG is gone, I guess the next best rust preventing grease is Cosmoline.
http://www.midwayusa.com/rewriteaproduct/267557
Rust inhibiting greases have additives which delay the migration of Oxygen through the grease. Wheel bearing lubes are lubricants. They are thick and heavy, but they are lubricants first and I doubt they have any rust inhibitors in them.
For my barrel storage, I clean the outside of the barrel. I wipe everything, interior and exterior, with an oily patch. Then I coat everything, inside and out, with RIG. (I still have a couple of cans).
Next I wrap the thing in wax paper, and use clear plastic tape to keep the wax paper from unraveling.
For collectable barrels, I go an additional step: I create a protective tube from PVC. I go to Home Depot, find a PVC tube in which the barrel fits snuggly. I buy the proper end caps. Once I cut the PVC tube to length, I glue one cap on one end. The other end, I tap on once the barrel is inside. I label the tube with magic marker.
The wax paper only has kept barrels perfect for ten years.