Pick one. You won't be able to tell any difference over the life of the gun, IMO.

I like Mobil 1 motor oil for pins and Mobil 1 grease for places I want the lube to stay put that I can get it on the surface. Some of the guys are using some kind of "turbine oil" and swear by it. I have an open quart of Mobil 1 motor oil and I'll think about switching when I use that quart up on my guns.