*giggles to self*
Ermm, typically white grease is just fine or any cheap general purpose grease. These aren't high speed bearings or close tolerance parts.
Use a thinner oil on the actually gear shafts / bearings / bushings as well. Keep it simple.
Tiger I - Panzer III - Panzer IV - Chi Nu Kai - Panther G - KV-1b 756(r)
M4A3(76) Sherman - T-34/85 - M3 Grant