Another vote for Mobtil 1 grease.Brother, you ask 20 people you will get 21 answers, I really like Lubriplate, but I have been using the same tube of Mobil 1 synthetic grease for years.
Automotive bearings generate lots of heat and this works great, I have never had a grease related failure.
Any grease will work, specific "gun" grease is more expensive then automotive grease. They will all work.
Unlike petroleum based greases it doesn't harden. I have Garands I've greased up and put away years ago and the grease is still as soft as when I applied it.