stu writes:

Are then any "greases" that are better than
others for this?

Define "better". Cheapest tub of bearing grease from Walmart is suitable.
Or the cheapest tub of petrolatum from the drug aisle. I use a spray can
of lithium grease just because it is easier to spread around. These all
have the sulfur largely removed so they smell better, versus the usual
cheap grease.