Not to be Capt. Obvious, but when it comes to grease on guns, one important thing is to clean out and replace regularly. Grease is an even better crud collector than oil.
But if one applies in moderation and cleans out and replaces after the gun is used, I'm fairly certain any number of greases from the gun-care aisle, auto store or hardware store will do the truck quite well.
I've seen threads on gun board go for pages, for instance, on what to use on choke tubes or which to use on trunions, knuckles and forearm irons on O/U shotguns. Fact is, it's a pretty low-demand application. Over the years, I've used a boatload of different things ranging from stuff specifically marked "choke tube lube" to white lithium to Mobil 1 to Zebco reel grease to Super Lube to Lubriplate. All of 'em, when changed out during routine cleaning, performed well. My quest for just the right product, IMO, was more or less pointless.
IMO, find something you like, and if you can save some bucks while at it, better yet.
And small tubes, though not cost efficient, are very nice for clean/lube kits that travel in the range or hunting bag, IMO. Of course, one can also buy a larger container to save a few bucks and transfer some into a little jar or into a syringe.
Again, though, I've found a syringe full or a tube of an ounce or so lasts a long, long time.