Guns actually have rather low friction points (except perhaps new Brownings) so just about any type of general grease will work. I believe the key is keeping the grease clean, not what type of grease is used. A tube of white grease that will fit into a caulk gun can be put into smaller containers and should last about 20 years.
Pro-shot Pro-Gold. Very sticky, stays in place well, good lubrication. Have also used lubriplate, which has good lubricating properties, but doesn't stay put nearly as well when the temperatures warm significantly.
I use absolutely NO grease on my guns. They get "Breakfree CLP" and nothing else. I use Scotts Liquid Gold furniture polish to wipe down the entire gun after cleaning. This has worked for me for many years of trapshooting, as well as many years spent in the marshes and on the bay hunting ducks and geese. NEVER had any rust problems at all, and guns stay well protected and lubed...Dan Thome (Trap2)