No clue what your particular Palmgren looks like, but if it's like mine of a similar size, it's a stone-stupid-simple design and once you knock the burrs off and straighten out the T-slots so they're actually usable, a dab of grease on the crude bearing surface under the table top and two dabs on the worm+wheel will suffice.
As to "which grease", any NGLI #2 or #3 grease "safe for red metal" will do. You don't need extreme pressure additives, any particular oil component viscosity, or any particular thickener type. It does not matter whether the oil component is a synthetic or a mineral oil. You probably won't encounter a grease based on a vegetable oil, but if you do, don't use it here. You do want a grease without additives that will corrode the bronze wheel/wheel.
Just make sure you clean all the old grease and lube out before putting in new grease. Greases of different thickener types can be very incompatible, "curdling" and becoming useless. Not an old wive's tale, there are charts to tell you which thickener types are compatible. But since you don't know the type of the old grease, and won't know the type of the new grease unless you read the really fine print, assume the old and new are worst enemies and clean out the old before putting in the new.