I use a waterproof bearing grease I have for repacking bicycle wheel bearings, but that's just because I have a big tube of it.
I stopped using it on handguns because I find grease gets very sticky in the cold and I get lots of failures to feed because it slows the slide when the temp gets down below 50 or so.
I only use grease on the Garand now and Eezox on handguns.
When I was a SIG guy, I always used TW25B. I still use it on pretty much everything. It is on the pricey side, but it takes such a small amount so it does go a long way.
Where I use grease, it's normally Lubriplate white lithium grease because that's what I have in the garage. I have a couple of those little GI grease bottles (the ones that fit in a M1 stock) in my range bag. I bought 4 dozen of those many years ago when they were selling for about 25 cents apiece.
Sentry Solutions Hi-Slip grease. Except Glocks where it is mentioned in the owner's manual to only use oil. And a very, very tiny amount of oil at that!
Mobil 1 grease is vastly cheaper and as good or better than any specialty gun grease. Go to your local parts store. It's less than $10 for a tub and will last the rest of your life. Also pick up a quart of Mobil 1 synthetic oil in 5w-30. Also cheap and enough to last the rest of your life unless you get into the gun cleaning business.