I would use a moly based bearing grease. This would be a dark gray grease. I have a bearing packer that looks like two cones on a threaded bolt that is hollow and has a grease fitting in the end. You put the bearing between the cones then pump grease into them with a grease gun. Valvoline makes a good moly based grease gun cartridge. I remember the red stuff and I don't remember it being that good of a grease. Moly is good stuff because it will lubricate even when the grease is gone and there is nothing left but a film. It is commonly used as a dry lubricant. Molybdenum disulphide is the long name and it is dark gray like graphite.
The type of grease is not as important as getting all the old grease out that is different.