Metal Gears = Tri-Flow grease
Plastic Gears = Tri-Flow grease or Singer white gear grease ( that's what Singer is selling in the tubes now )
Singer Motors = Singer Motor Lube in the tube ( grease ) if you can get some. It's discontinued. Otherwise petroleum jelly.
Yes it melts and gets soft when it gets warm, that is the exact same thing the Singer motor lube does. It has to to flow to the bearings.
Other motors with grease pots = petroleum jelly or what ever the owners manual says to use. Many actually state to use petroleum jelly.
Motors with oil holes = Regular clear sewing machine oil.
Joe